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Tietze's theorem #971
Tietze's theorem #971
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Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com>
Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com>
Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com>
Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com>
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I re-read the scripts and could find a number of shortcuts that I have committed.
What about using notations such as:
Local Notation "'2/3" := (PosNum twothirds_pos).
in continuous_bounded_extension
?
That could make intermediate goals a bit shorter and more readable.
(Yet, inside this proof the problem is not here ^_^.)
Turns out |
* tietze lemma done * nearly done with tietze * cauchy with admits * cauchy part done * tietze continuity done * tietze bounded * proof of tietze is done * linting and changelog * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * handling interval shifting inside tietze * simplifying a bit calculations * shorten proofs, nitpicking * positive 3 notation --------- Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
* tietze lemma done * nearly done with tietze * cauchy with admits * cauchy part done * tietze continuity done * tietze bounded * proof of tietze is done * linting and changelog * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * handling interval shifting inside tietze * simplifying a bit calculations * shorten proofs, nitpicking * positive 3 notation --------- Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
* tietze lemma done * nearly done with tietze * cauchy with admits * cauchy part done * tietze continuity done * tietze bounded * proof of tietze is done * linting and changelog * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * Update theories/numfun.v Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> * handling interval shifting inside tietze * simplifying a bit calculations * shorten proofs, nitpicking * positive 3 notation --------- Co-authored-by: affeldt-aist <33154536+affeldt-aist@users.noreply.github.com> Co-authored-by: Reynald Affeldt <reynald.affeldt@aist.go.jp>
Motivation for this change
In the apparently never-ending results needed for fundamental theorem, here's Tietze's Extension theorem. We're continuing along #965 to show that continuous functions are dense in L1.
A few things to note:
X
is normal. Here, we assume it has urysohn extensions. Urysohn's lemma (Urysohn's Lemma #900) is the proof that these are equivalent. We could directly show that pseudometric spaces have urysohn extensions, once we get that far if we had to. Or we can merge in the urysohns' lemma PR, move to HB, and just do it that way.f
withx/(1+|x|)
and applying the bounded version. We don't need it right now, so we can deal with that later.posnum
stuff automating away several days of work!Things done/to do
CHANGELOG_UNRELEASED.md
Compatibility with MathComp 2.0
TODO: HB port
to make sure someone ports this PR tothe
hierarchy-builder
branch or I already opened an issue or PR (please cross reference).Automatic note to reviewers
Read this Checklist and put a milestone if possible.