T82: locally euclidean => locally arc connected#272
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* fix line ending issues * fix: add ref name to mathse ref See pi-base/web#10 * Update CONTRIBUTING.md * Weak Hausdorff property (#237) * Weak Hausdorff property * Add properties for weak Hausdorff * T227: tweak the explanation * add kspace properties and theorems (#236) * add kspace properites and theorems * tweaking the definitions * Update P000141.md * Update P000140.md --------- Co-authored-by: Patrick Rabau <prabau@sbcglobal.net> * S37: example of US, non weak Hausdorff space (#241) * Fix typo in P84 * Add results to show that pseudometrizable implies 1st countable (#244) * Add results to show that pseudometrizable implies 1st countable * fix T327 id * fix typos in P144 * add mathse reference * Fix typo * Update T000327.md * Some theorems and traits involving local metrizability (#248) * More theorems about locally pseudometrizable (#250) * More theorems about locally pseudometrizable * T331 converse * Misc spaces: more precise position between T1 and T2 (#249) * Misc spaces: more precise position between T1 and T2 * remove unneeded T2 assertion * remove another unneeded T2 assumption --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * T328 update (#252) * Included locally Euclidean -> locally compact to get some examples of spaces which are locally metrizable but not locally Euclidean. * fixed parse error * fixed another typo * suggested edits * Use citation cff (#253) * Commit line-ending changes auto-enforced by git * Adds a CITATION.cff file to make use of the github citation button feature https://docs.github.com/en/repositories/managing-your-repositorys-settings-and-features/customizing-your-repository/about-citation-files * Update CITATION.cff --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * T230: first countable + US imply T2 (#257) * T230: first countable + US imply T2 * remove deduceable T1 --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * Update CITATION.cff (#260) * T209 generalization (#264) * T209 generalization * fix typo * T208: indiscrete + distinct points ==> no isolated point (#266) * S27 and S28 updates (#261) * S27 updates * S28 updates * fix typo * S27/P23: added reference * S31: square of one point compactification of Q (#263) * S153: Open long ray (#270) * S153: Open long ray * improve lindelof->weakly lindelof --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * split up theorems implying conjunctions of properties (#267) * split up theorems implying conjuctions of properties * remove proposed but out-of-syntax deprecatedBy * Update T000042.md * Update T000099.md * Update T000100.md * add converse * Delete T000171.md * Update T000176.md * Update T001042.md * Update T001176.md * fix typos * split T104 * fix uid * consolidate theorem IDs * add a few converses --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * more inclusive choice of default terminology (#271) * more inclusive choice of default terminology * Update README.md * Update README.md * Update README.md * add sequential property to arens space (#274) * T82: locally euclidean => locally arc connected (#272) * connect rothberger property and create counterexamples (#275) * Update P000144.md * Fix P144 line ending * fix MR refs * Fix more MR refs * add aliases for separation properties (#276) * improve regular to t3 (#277) * improve regular to t3 * improve t3 to t3.5 for S77 (and add t5 for P63) * add michael line S63 normality props * swap the factors to map S&S --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> --------- Co-authored-by: James Dabbs <james.dabbs@gmail.com> Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> Co-authored-by: Patrick Rabau <prabau@sbcglobal.net> Co-authored-by: Chris <30360237+ccaruvana@users.noreply.github.com> Co-authored-by: rschwiebert <rschwiebert@users.noreply.github.com>
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* fix line ending issues * fix: add ref name to mathse ref See pi-base/web#10 * Update CONTRIBUTING.md * Weak Hausdorff property (#237) * Weak Hausdorff property * Add properties for weak Hausdorff * T227: tweak the explanation * add kspace properties and theorems (#236) * add kspace properites and theorems * tweaking the definitions * Update P000141.md * Update P000140.md --------- Co-authored-by: Patrick Rabau <prabau@sbcglobal.net> * S37: example of US, non weak Hausdorff space (#241) * Fix typo in P84 * Add results to show that pseudometrizable implies 1st countable (#244) * Add results to show that pseudometrizable implies 1st countable * fix T327 id * fix typos in P144 * add mathse reference * Fix typo * Update T000327.md * Some theorems and traits involving local metrizability (#248) * More theorems about locally pseudometrizable (#250) * More theorems about locally pseudometrizable * T331 converse * Misc spaces: more precise position between T1 and T2 (#249) * Misc spaces: more precise position between T1 and T2 * remove unneeded T2 assertion * remove another unneeded T2 assumption --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * T328 update (#252) * Included locally Euclidean -> locally compact to get some examples of spaces which are locally metrizable but not locally Euclidean. * fixed parse error * fixed another typo * suggested edits * Use citation cff (#253) * Commit line-ending changes auto-enforced by git * Adds a CITATION.cff file to make use of the github citation button feature https://docs.github.com/en/repositories/managing-your-repositorys-settings-and-features/customizing-your-repository/about-citation-files * Update CITATION.cff --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * T230: first countable + US imply T2 (#257) * T230: first countable + US imply T2 * remove deduceable T1 --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * Update CITATION.cff (#260) * T209 generalization (#264) * T209 generalization * fix typo * T208: indiscrete + distinct points ==> no isolated point (#266) * S27 and S28 updates (#261) * S27 updates * S28 updates * fix typo * S27/P23: added reference * S31: square of one point compactification of Q (#263) * S153: Open long ray (#270) * S153: Open long ray * improve lindelof->weakly lindelof --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * split up theorems implying conjunctions of properties (#267) * split up theorems implying conjuctions of properties * remove proposed but out-of-syntax deprecatedBy * Update T000042.md * Update T000099.md * Update T000100.md * add converse * Delete T000171.md * Update T000176.md * Update T001042.md * Update T001176.md * fix typos * split T104 * fix uid * consolidate theorem IDs * add a few converses --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * more inclusive choice of default terminology (#271) * more inclusive choice of default terminology * Update README.md * Update README.md * Update README.md * add sequential property to arens space (#274) * T82: locally euclidean => locally arc connected (#272) * connect rothberger property and create counterexamples (#275) * Update P000144.md * Fix P144 line ending * fix MR refs * Fix more MR refs * add aliases for separation properties (#276) * improve regular to t3 (#277) * improve regular to t3 * improve t3 to t3.5 for S77 (and add t5 for P63) * add michael line S63 normality props * swap the factors to map S&S --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * add counterexample from https://math.stackexchange.com/q/3145712 (#279) * add counterexample * Update README.md * remove T0 assumption in T23 (#283) * remove T0 assumption in T23 * actually update T23 * Update T000023.md --------- Co-authored-by: James Dabbs <james.dabbs@gmail.com> Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> Co-authored-by: Patrick Rabau <prabau@sbcglobal.net> Co-authored-by: Chris <30360237+ccaruvana@users.noreply.github.com> Co-authored-by: rschwiebert <rschwiebert@users.noreply.github.com>
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* fix line ending issues * fix: add ref name to mathse ref See pi-base/web#10 * Update CONTRIBUTING.md * Weak Hausdorff property (#237) * Weak Hausdorff property * Add properties for weak Hausdorff * T227: tweak the explanation * add kspace properties and theorems (#236) * add kspace properites and theorems * tweaking the definitions * Update P000141.md * Update P000140.md --------- Co-authored-by: Patrick Rabau <prabau@sbcglobal.net> * S37: example of US, non weak Hausdorff space (#241) * Fix typo in P84 * Add results to show that pseudometrizable implies 1st countable (#244) * Add results to show that pseudometrizable implies 1st countable * fix T327 id * fix typos in P144 * add mathse reference * Fix typo * Update T000327.md * Some theorems and traits involving local metrizability (#248) * More theorems about locally pseudometrizable (#250) * More theorems about locally pseudometrizable * T331 converse * Misc spaces: more precise position between T1 and T2 (#249) * Misc spaces: more precise position between T1 and T2 * remove unneeded T2 assertion * remove another unneeded T2 assumption --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * T328 update (#252) * Included locally Euclidean -> locally compact to get some examples of spaces which are locally metrizable but not locally Euclidean. * fixed parse error * fixed another typo * suggested edits * Use citation cff (#253) * Commit line-ending changes auto-enforced by git * Adds a CITATION.cff file to make use of the github citation button feature https://docs.github.com/en/repositories/managing-your-repositorys-settings-and-features/customizing-your-repository/about-citation-files * Update CITATION.cff --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * T230: first countable + US imply T2 (#257) * T230: first countable + US imply T2 * remove deduceable T1 --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * Update CITATION.cff (#260) * T209 generalization (#264) * T209 generalization * fix typo * T208: indiscrete + distinct points ==> no isolated point (#266) * S27 and S28 updates (#261) * S27 updates * S28 updates * fix typo * S27/P23: added reference * S31: square of one point compactification of Q (#263) * S153: Open long ray (#270) * S153: Open long ray * improve lindelof->weakly lindelof --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * split up theorems implying conjunctions of properties (#267) * split up theorems implying conjuctions of properties * remove proposed but out-of-syntax deprecatedBy * Update T000042.md * Update T000099.md * Update T000100.md * add converse * Delete T000171.md * Update T000176.md * Update T001042.md * Update T001176.md * fix typos * split T104 * fix uid * consolidate theorem IDs * add a few converses --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * more inclusive choice of default terminology (#271) * more inclusive choice of default terminology * Update README.md * Update README.md * Update README.md * add sequential property to arens space (#274) * T82: locally euclidean => locally arc connected (#272) * connect rothberger property and create counterexamples (#275) * Update P000144.md * Fix P144 line ending * fix MR refs * Fix more MR refs * add aliases for separation properties (#276) * improve regular to t3 (#277) * improve regular to t3 * improve t3 to t3.5 for S77 (and add t5 for P63) * add michael line S63 normality props * swap the factors to map S&S --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * add counterexample from https://math.stackexchange.com/q/3145712 (#279) * add counterexample * Update README.md * remove T0 assumption in T23 (#283) * remove T0 assumption in T23 * actually update T23 * Update T000023.md * add paracompact properties and arens space props (#282) * add paracompact properites and arens space props * Update P000050.md * Update P000146.md * misc changes * add alternate def for ultraparacompact --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * Some more properties for the Arens space (#285) * More Arens space updates * fix for scattered property --------- Co-authored-by: James Dabbs <james.dabbs@gmail.com> Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> Co-authored-by: Patrick Rabau <prabau@sbcglobal.net> Co-authored-by: Chris <30360237+ccaruvana@users.noreply.github.com> Co-authored-by: rschwiebert <rschwiebert@users.noreply.github.com>
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* fix line ending issues * fix: add ref name to mathse ref See pi-base/web#10 * Update CONTRIBUTING.md * Weak Hausdorff property (#237) * Weak Hausdorff property * Add properties for weak Hausdorff * T227: tweak the explanation * add kspace properties and theorems (#236) * add kspace properites and theorems * tweaking the definitions * Update P000141.md * Update P000140.md --------- Co-authored-by: Patrick Rabau <prabau@sbcglobal.net> * S37: example of US, non weak Hausdorff space (#241) * Fix typo in P84 * Add results to show that pseudometrizable implies 1st countable (#244) * Add results to show that pseudometrizable implies 1st countable * fix T327 id * fix typos in P144 * add mathse reference * Fix typo * Update T000327.md * Some theorems and traits involving local metrizability (#248) * More theorems about locally pseudometrizable (#250) * More theorems about locally pseudometrizable * T331 converse * Misc spaces: more precise position between T1 and T2 (#249) * Misc spaces: more precise position between T1 and T2 * remove unneeded T2 assertion * remove another unneeded T2 assumption --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * T328 update (#252) * Included locally Euclidean -> locally compact to get some examples of spaces which are locally metrizable but not locally Euclidean. * fixed parse error * fixed another typo * suggested edits * Use citation cff (#253) * Commit line-ending changes auto-enforced by git * Adds a CITATION.cff file to make use of the github citation button feature https://docs.github.com/en/repositories/managing-your-repositorys-settings-and-features/customizing-your-repository/about-citation-files * Update CITATION.cff --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * T230: first countable + US imply T2 (#257) * T230: first countable + US imply T2 * remove deduceable T1 --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * Update CITATION.cff (#260) * T209 generalization (#264) * T209 generalization * fix typo * T208: indiscrete + distinct points ==> no isolated point (#266) * S27 and S28 updates (#261) * S27 updates * S28 updates * fix typo * S27/P23: added reference * S31: square of one point compactification of Q (#263) * S153: Open long ray (#270) * S153: Open long ray * improve lindelof->weakly lindelof --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * split up theorems implying conjunctions of properties (#267) * split up theorems implying conjuctions of properties * remove proposed but out-of-syntax deprecatedBy * Update T000042.md * Update T000099.md * Update T000100.md * add converse * Delete T000171.md * Update T000176.md * Update T001042.md * Update T001176.md * fix typos * split T104 * fix uid * consolidate theorem IDs * add a few converses --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * more inclusive choice of default terminology (#271) * more inclusive choice of default terminology * Update README.md * Update README.md * Update README.md * add sequential property to arens space (#274) * T82: locally euclidean => locally arc connected (#272) * connect rothberger property and create counterexamples (#275) * Update P000144.md * Fix P144 line ending * fix MR refs * Fix more MR refs * add aliases for separation properties (#276) * improve regular to t3 (#277) * improve regular to t3 * improve t3 to t3.5 for S77 (and add t5 for P63) * add michael line S63 normality props * swap the factors to map S&S --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * add counterexample from https://math.stackexchange.com/q/3145712 (#279) * add counterexample * Update README.md * remove T0 assumption in T23 (#283) * remove T0 assumption in T23 * actually update T23 * Update T000023.md * add paracompact properties and arens space props (#282) * add paracompact properites and arens space props * Update P000050.md * Update P000146.md * misc changes * add alternate def for ultraparacompact --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * Some more properties for the Arens space (#285) * More Arens space updates * fix for scattered property * Fix for Fully normal (P34) (#289) * Fix for Fully normal (P34) * add one reference * generalize T214 from fully T4 to fully normal (#288) --------- Co-authored-by: James Dabbs <james.dabbs@gmail.com> Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> Co-authored-by: Patrick Rabau <prabau@sbcglobal.net> Co-authored-by: Chris <30360237+ccaruvana@users.noreply.github.com> Co-authored-by: rschwiebert <rschwiebert@users.noreply.github.com>
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* fix line ending issues * fix: add ref name to mathse ref See pi-base/web#10 * Update CONTRIBUTING.md * Weak Hausdorff property (#237) * Weak Hausdorff property * Add properties for weak Hausdorff * T227: tweak the explanation * add kspace properties and theorems (#236) * add kspace properites and theorems * tweaking the definitions * Update P000141.md * Update P000140.md --------- Co-authored-by: Patrick Rabau <prabau@sbcglobal.net> * S37: example of US, non weak Hausdorff space (#241) * Fix typo in P84 * Add results to show that pseudometrizable implies 1st countable (#244) * Add results to show that pseudometrizable implies 1st countable * fix T327 id * fix typos in P144 * add mathse reference * Fix typo * Update T000327.md * Some theorems and traits involving local metrizability (#248) * More theorems about locally pseudometrizable (#250) * More theorems about locally pseudometrizable * T331 converse * Misc spaces: more precise position between T1 and T2 (#249) * Misc spaces: more precise position between T1 and T2 * remove unneeded T2 assertion * remove another unneeded T2 assumption --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * T328 update (#252) * Included locally Euclidean -> locally compact to get some examples of spaces which are locally metrizable but not locally Euclidean. * fixed parse error * fixed another typo * suggested edits * Use citation cff (#253) * Commit line-ending changes auto-enforced by git * Adds a CITATION.cff file to make use of the github citation button feature https://docs.github.com/en/repositories/managing-your-repositorys-settings-and-features/customizing-your-repository/about-citation-files * Update CITATION.cff --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * T230: first countable + US imply T2 (#257) * T230: first countable + US imply T2 * remove deduceable T1 --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * Update CITATION.cff (#260) * T209 generalization (#264) * T209 generalization * fix typo * T208: indiscrete + distinct points ==> no isolated point (#266) * S27 and S28 updates (#261) * S27 updates * S28 updates * fix typo * S27/P23: added reference * S31: square of one point compactification of Q (#263) * S153: Open long ray (#270) * S153: Open long ray * improve lindelof->weakly lindelof --------- Co-authored-by: Steven Clontz <steven.clontz@gmail.com> * split up theorems implying conjunctions of properties (#267) * split up theorems implying conjuctions of properties * remove proposed but out-of-syntax deprecatedBy * Update T000042.md * Update T000099.md * Update T000100.md * add converse * Delete T000171.md * Update T000176.md * Update T001042.md * Update T001176.md * fix typos * split T104 * fix uid * consolidate theorem IDs * add a few converses --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * more inclusive choice of default terminology (#271) * more inclusive choice of default terminology * Update README.md * Update README.md * Update README.md * add sequential property to arens space (#274) * T82: locally euclidean => locally arc connected (#272) * connect rothberger property and create counterexamples (#275) * Update P000144.md * Fix P144 line ending * fix MR refs * Fix more MR refs * add aliases for separation properties (#276) * improve regular to t3 (#277) * improve regular to t3 * improve t3 to t3.5 for S77 (and add t5 for P63) * add michael line S63 normality props * swap the factors to map S&S --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * add counterexample from https://math.stackexchange.com/q/3145712 (#279) * add counterexample * Update README.md * remove T0 assumption in T23 (#283) * remove T0 assumption in T23 * actually update T23 * Update T000023.md * add paracompact properties and arens space props (#282) * add paracompact properites and arens space props * Update P000050.md * Update P000146.md * misc changes * add alternate def for ultraparacompact --------- Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> * Some more properties for the Arens space (#285) * More Arens space updates * fix for scattered property * Fix for Fully normal (P34) (#289) * Fix for Fully normal (P34) * add one reference * generalize T214 from fully T4 to fully normal (#288) * Add a perfectly normal, non fully normal space (#287) * add perfectly normal non fully normal space * Update README.md * Updates to Fortissimo space (S22) (#292) * Some theorems involving compactly generated (#290) * Some theorems involving compactly generated * Example of space with P140 and not P141 * T70 to provide spaces with P141 and not P142 * Better version of T70 * change the ref for T70 * Convenience aliases for compactly generated (#293) * Updates to Single ultrafilter topology (#294) --------- Co-authored-by: James Dabbs <james.dabbs@gmail.com> Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com> Co-authored-by: Patrick Rabau <prabau@sbcglobal.net> Co-authored-by: Chris <30360237+ccaruvana@users.noreply.github.com> Co-authored-by: rschwiebert <rschwiebert@users.noreply.github.com>
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@ccaruvana Another one related to locally Euclidean.
Will deduce locally arc connected for S153 and S170:
https://topology.pi-base.org/spaces?q=Locally%20Euclidean%2BLocally%20Arc%20Connected