diff --git a/spaces/S000107/properties/P000026.md b/spaces/S000107/properties/P000026.md deleted file mode 100644 index 24fc626073..0000000000 --- a/spaces/S000107/properties/P000026.md +++ /dev/null @@ -1,10 +0,0 @@ ---- -space: S000107 -property: P000026 -value: false -refs: -- doi: 10.1007/978-1-4612-6290-9_6 - name: Counterexamples in Topology ---- - -See item #7 for space #109 in {{doi:10.1007/978-1-4612-6290-9_6}}. diff --git a/spaces/S000107/properties/P000028.md b/spaces/S000107/properties/P000028.md deleted file mode 100644 index 74ce8cccaa..0000000000 --- a/spaces/S000107/properties/P000028.md +++ /dev/null @@ -1,10 +0,0 @@ ---- -space: S000107 -property: P000028 -value: false -refs: -- doi: 10.1007/978-1-4612-6290-9_6 - name: Counterexamples in Topology ---- - -See item #6 for space #109 in {{doi:10.1007/978-1-4612-6290-9_6}}. diff --git a/spaces/S000107/properties/P000129.md b/spaces/S000107/properties/P000129.md deleted file mode 100644 index 0cfa704ad4..0000000000 --- a/spaces/S000107/properties/P000129.md +++ /dev/null @@ -1,7 +0,0 @@ ---- -space: S000107 -property: P000129 -value: false ---- - -The space is non-trivial by definition. diff --git a/spaces/S000107/properties/P000187.md b/spaces/S000107/properties/P000187.md new file mode 100644 index 0000000000..f74495beb9 --- /dev/null +++ b/spaces/S000107/properties/P000187.md @@ -0,0 +1,21 @@ +--- +space: S000107 +property: P000187 +value: false +refs: +- mathse: 4973385 + name: Answer to "Are W-spaces with countable pseudocharacter first + countable?" +--- + +Note that the {P187} property is hereditary. + +Let $f_{m,n}:\omega\to\mathbb R$ be defined by +$f_{m,n}(m)=\frac{1}{m+2}$ and $f_{m,n}(k)=0$ otherwise. + +The result follows as the subspace +$\{\vec 0\}\cup\{f_{m,n}:m,n<\omega\}$ is homeomorphic to +{S131} +and {S131|P187}. + +See {{mathse:4973385}}. diff --git a/spaces/S000107/properties/P000191.md b/spaces/S000107/properties/P000191.md new file mode 100644 index 0000000000..398d4a5bad --- /dev/null +++ b/spaces/S000107/properties/P000191.md @@ -0,0 +1,14 @@ +--- +space: S000107 +property: P000191 +value: true +refs: +- mathse: 1644041 + name: Answer to "Familiar spaces in which every one point set is Gδ + but space is not first countable" +--- + +Each $f:\omega\to\mathbb R$ is the countable intersection of +$\bigcap_{m<\omega}\prod_{n<\omega}(f(n)-\frac{1}{m+1},f(n)+\frac{1}{m+1})$. + +See {{mathse:1644041}}.