List questions from first-countable | MathQa

First countable + separable imply second countable?

Published on 12 Jan 2025 - 23:09

Familiar spaces in which every one point set is $G_\delta$ but space is not first countable

Published on 12 Jan 2025 - 23:28

A non metric first countable topological space

Published on 12 Jan 2025 - 23:08

Properties of Infinite set on co-finite topology and Countable set on co-countable topology

Published on 12 Jan 2025 - 23:28

A neighborhood basis in an arbitrary topological space for which the inclusion is a total order

Published on 12 Jan 2025 - 23:29

Proof for sequentially continuous function with a first countable domain is continuous

Published on 12 Jan 2025 - 23:27

Is $\mathbb{Q}^n$ countable?

Published on 12 Jan 2025 - 17:30

Proof that the quotient space of $\mathbb{R}^2/L$ where $L$ is a line passing through the origin is not first countable

Published on 12 Jan 2025 - 23:31

Cofinite topology if first countable iff $X$ is countable

Published on 12 Jan 2025 - 23:14

Showing that a first countable space is Hausdorff if and only if every sequence converging in $X$ has a unique limit

Published on 12 Jan 2025 - 23:31