box product of reals is not W but has points Gdelta

spaces/S000107/properties/P000187.md

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+---
+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}}.

spaces/S000107/properties/P000191.md

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+---
+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}}.