List questions from general-topology | MathQA

If $X$ is compact and $Y$ is closed. Show that there exists $x_0 \in X$, and $y_0 \in Y$ such that $|x_0-y_0| \leq |x-y|$ for all $x \in X$, $y \in Y$

Published on 29 Mar 2018 - 21:09

Homeomorphism between open unit balls from equivalent distances

Published on 29 Mar 2018 - 21:26

Properties of $\tau_1 \lor \tau_2$

Published on 30 Mar 2018 - 2:43

construct a basis of a given topology.

Published on 30 Mar 2018 - 3:50

Can someone please verify this proof of mine relating limit points and closure of sets?

Published on 30 Mar 2026 - 3:55

$B \subseteq \mathbb{R}^2$ is simply connected. Is $B + [-1,1]^2$ still simply connected?

Published on 30 Mar 2018 - 10:04

Intersection of countable collection of closed intervals

Published on 30 Mar 2018 - 11:22

Nonexistence of a homeomorphism between a open set and the unit sphere

Published on 25 Mar 2026 - 17:32

For a continuous function defined on [a,b] , is the set of points at which f(x)>d closed set?

Published on 22 Mar 2026 - 17:56

Mapping $U$ homeomorphically onto $f(U)$.

Published on 30 Mar 2018 - 13:15

Open subsets of a irreducible topological space

Published on 30 Mar 2026 - 1:51

Why is the hyperbolic plane homeomorphic to $\mathbb{R}^2$, whilst the 2-sphere isn't?

Published on 31 Mar 2026 - 3:10

Are these metrics equivalents?

Published on 31 Mar 2026 - 20:25

About continuous extensions and retractions

Published on 23 Mar 2026 - 0:19

Showing that a CW complex is compactly generated

Published on 23 Mar 2026 - 0:56