From 8d6dfd8f9957a49c9373619278017840b90eaecc Mon Sep 17 00:00:00 2001 From: Steven Clontz Date: Tue, 15 Oct 2024 16:55:10 -0500 Subject: [PATCH] add S185|P130 false (#803) * add S185|P130 false * Update P000130.md --- spaces/S000185/properties/P000130.md | 11 +++++++++++ 1 file changed, 11 insertions(+) create mode 100644 spaces/S000185/properties/P000130.md diff --git a/spaces/S000185/properties/P000130.md b/spaces/S000185/properties/P000130.md new file mode 100644 index 000000000..ee8afb372 --- /dev/null +++ b/spaces/S000185/properties/P000130.md @@ -0,0 +1,11 @@ +--- +space: S000185 +property: P000130 +value: false +refs: +- mathse: 4985015 + name: Answer to "Is every second-countable weakly locally compact space also locally compact?" +--- + +Consider a neighborhood $U$ of $\infty_x$ missing $\infty_y$, and any neighborhood $V\subseteq U$ of $\infty_x$. +Then $V$ contains a column of $\omega^2$, which is closed and discrete in $V$, showing $V$ is not compact.