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+---
+space: S000185
+property: P000130
+value: false
+refs:
+- mathse: 4985014
+  name: 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.
+
+See {{mathse:4985014}}.