Question

Compactness of spaces

score 99 · Answer 1 · 2026-04-11 06:50:32

99

Views

Compactness of spaces

Published on 11 Apr 2026 - 6:50

score 487 · Answer 2 · 2026-04-14 11:51:15

487

Views

Every compact convex set in $\mathbb{C}$ is the intersection of all closed half-space containing it

Published on 14 Apr 2026 - 11:51

score 1.1k · Answer 3 · 2026-04-12 17:46:57

1.1k

Views

Inverse of a injective continuous map defined on a compact set is continuous.

Published on 12 Apr 2026 - 17:46

score 233 · Answer 4 · 2026-04-16 10:11:03

233

Views

Let $K$ be a compact subset of $X$ and $E ⊂ K$. Suppose that $E$ is closed relative to $K$. Prove or disprove that $E$ is closed relative to $X$.

Published on 16 Apr 2026 - 10:11

score 204 · Answer 5 · 2026-04-15 18:09:57

204

Views

Prove that there exists $\epsilon > 0$ such that $A:= \{v \in \mathbb{R}^n \mid d(v,B) \leq \epsilon\} \subseteq E$

Published on 15 Apr 2026 - 18:09

score 626 · Answer 6 · 2026-04-14 13:30:42

626

Views

If $X$ and $Y$ are compact subsets of $\mathbb R^n$, then $X+Y$ is compact.

Published on 14 Apr 2026 - 13:30

score 47 · Answer 7 · 2026-05-11 08:38:38

47

Views

$ A \subset \Bbb R$ is bounded and not compact, exhibit $f: A \to \Bbb R$ that isn't bounded

Published on 11 May 2026 - 8:38

score 680 · Answer 8 · 2026-05-10 14:07:48

680

Views

Prove the metric induced topology is the same as the product topology

Published on 10 May 2026 - 14:07

score 687 · Answer 9 · 2026-04-11 14:35:40

687

Views

Infinite Subset of a Metric Space is Not Compact

Published on 11 Apr 2026 - 14:35

score 366 · Answer 10 · 2026-05-10 16:57:05

366

Views

Preimage of the Real Line

Published on 10 May 2026 - 16:57

score 72 · Answer 11 · 2026-04-09 03:51:45

72

Views

Compact covering of a compact set.

Published on 09 Apr 2026 - 3:51

score 387 · Answer 12 · 2026-04-13 18:38:34

387

Views

Continuous Functions on Compact Sets and Maximal Values

Published on 13 Apr 2026 - 18:38

score 5.2k · Answer 13 · 2026-04-14 22:41:05

5.2k

Views

Infinite metric space with discrete metric is not compact

Published on 14 Apr 2026 - 22:41

score 403 · Answer 14 · 2026-04-11 01:44:27

403

Views

Compact Sets and Continuous Functions

Published on 11 Apr 2026 - 1:44

score 1.4k · Answer 15 · 2026-04-11 23:12:12

1.4k

Views

Is $[0,1]$ a compact subspace of $\mathbb R$ in the cocountable topology?

Published on 11 Apr 2026 - 23:12

List Question

Compactness of spaces

Every compact convex set in $\mathbb{C}$ is the intersection of all closed half-space containing it

Inverse of a injective continuous map defined on a compact set is continuous.

Let $K$ be a compact subset of $X$ and $E ⊂ K$. Suppose that $E$ is closed relative to $K$. Prove or disprove that $E$ is closed relative to $X$.

Prove that there exists $\epsilon > 0$ such that $A:= \{v \in \mathbb{R}^n \mid d(v,B) \leq \epsilon\} \subseteq E$

If $X$ and $Y$ are compact subsets of $\mathbb R^n$, then $X+Y$ is compact.

$ A \subset \Bbb R$ is bounded and not compact, exhibit $f: A \to \Bbb R$ that isn't bounded

Prove the metric induced topology is the same as the product topology

Infinite Subset of a Metric Space is Not Compact

Preimage of the Real Line

Compact covering of a compact set.

Continuous Functions on Compact Sets and Maximal Values

Infinite metric space with discrete metric is not compact

Compact Sets and Continuous Functions

Is $[0,1]$ a compact subspace of $\mathbb R$ in the cocountable topology?

Trending Questions

Popular # Hahtags

Popular Questions