Question

Compactness of spaces

score 96 · Answer 1 · 2018-04-06 15:07:58

96

Views

Compactness of spaces

Published on 06 Apr 2018 - 15:07

score 485 · Answer 2 · 2018-04-07 15:10:05

485

Views

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

Published on 07 Apr 2018 - 15:10

score 1.1k · Answer 3 · 2018-04-07 23:41:24

1.1k

Views

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

Published on 07 Apr 2018 - 23:41

score 230 · Answer 4 · 2018-04-08 11:04:40

230

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 08 Apr 2018 - 11:04

score 201 · Answer 5 · 2018-04-09 11:22:04

201

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 09 Apr 2018 - 11:22

score 623 · Answer 6 · 2018-04-10 05:23:21

623

Views

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

Published on 10 Apr 2018 - 5:23

score 44 · Answer 7 · 2026-03-25 19:25:20

44

Views

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

Published on 25 Mar 2026 - 19:25

score 677 · Answer 8 · 2026-03-25 06:06:21

677

Views

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

Published on 25 Mar 2026 - 6:06

score 684 · Answer 9 · 2018-04-10 22:08:15

684

Views

Infinite Subset of a Metric Space is Not Compact

Published on 10 Apr 2018 - 22:08

score 362 · Answer 10 · 2026-03-26 19:24:44

362

Views

Preimage of the Real Line

Published on 26 Mar 2026 - 19:24

score 69 · Answer 11 · 2018-04-12 02:35:43

69

Views

Compact covering of a compact set.

Published on 12 Apr 2018 - 2:35

score 384 · Answer 12 · 2018-04-12 03:09:10

384

Views

Continuous Functions on Compact Sets and Maximal Values

Published on 12 Apr 2018 - 3:09

score 5.2k · Answer 13 · 2018-04-12 05:20:38

5.2k

Views

Infinite metric space with discrete metric is not compact

Published on 12 Apr 2018 - 5:20

score 400 · Answer 14 · 2018-04-12 06:09:45

400

Views

Compact Sets and Continuous Functions

Published on 12 Apr 2018 - 6:09

score 1.4k · Answer 15 · 2018-04-12 11:18:10

1.4k

Views

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

Published on 12 Apr 2018 - 11:18

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?

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