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 21 Aug 2022 - 8:44

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

Published on 09 Sep 2022 - 22:51

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

Published on 13 Sep 2022 - 10:47

Confusion about a proof of Lusin's theorem

Published on 26 Sep 2022 - 13:45

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

Published on 09 Oct 2022 - 21:12

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

Published on 08 Nov 2022 - 15:11

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

Published on 14 Nov 2022 - 18:44

Proof verification for separable metric space implies second countable.

Published on 22 Dec 2022 - 21:20

Proof verifying that separable metric space is second countable

Published on 01 Jan 2023 - 19:01