List questions from second-countable | MathQA

Borel $\sigma$-algebra with $\sigma$-finite measure: does a function vanish almost everywhere outside its essential support?

Published on 26 Mar 2026 - 8:04

$(\Bbb R, \tau)$ with $\tau$ defined as: $U\in \tau \iff U=\emptyset \vee 0 \in U$ is not second-countable.

Published on 26 Mar 2026 - 6:22

Is the Alexandroff extension of a locally compact, second-countable space second-countable?

Published on 26 Mar 2026 - 6:25

Confusion about a proof of Lusin's theorem

Published on 26 Mar 2026 - 6:21

The Borel $\sigma$-algebra generated by the product topology coincides with the product of Borel $\sigma$-algebras: where did I get wrong?

Published on 15 Apr 2026 - 22:02

Compact Hausdorff Space - X Second Countable iff C(X) separable

Published on 26 Mar 2026 - 6:18

Let $X$ be a topological space that satisfies the second axiom of countability. Show that if ...

Published on 26 Mar 2026 - 6:22

Proof verification for separable metric space implies second countable.

Published on 26 Mar 2026 - 6:19

Proof verifying that separable metric space is second countable

Published on 26 Mar 2026 - 6:19