Question

Proving sequence of half isometries on a compact has converging subsequence to fixed point

score 39 · Answer 1 · 2026-03-25 10:55:25

39

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Proving sequence of half isometries on a compact has converging subsequence to fixed point

Published on 25 Mar 2026 - 10:55

score 228 · Answer 2 · 2018-05-20 21:07:09

228

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Open subset of locally compact non Hausdorff space which is not locally compact.

Published on 20 May 2018 - 21:07

score 556 · Answer 3 · 2026-03-25 07:43:17

556

Views

For which n differential operator $C^{(n)}[0, 1] \rightarrow C[0,1]$ is compact

Published on 25 Mar 2026 - 7:43

score 421 · Answer 4 · 2018-05-21 03:13:11

421

Views

Prove that $\mathbb{Z}^+$ is not compact with the arithmetic progression topology

Published on 21 May 2018 - 3:13

score 61 · Answer 5 · 2026-03-28 02:04:32

61

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Question about different topologies on spaces of continuous functions.

Published on 28 Mar 2026 - 2:04

score 44 · Answer 6 · 2026-03-27 17:34:11

44

Views

How to prove that following set is not locally compact.

Published on 27 Mar 2026 - 17:34

score 303 · Answer 7 · 2026-03-25 16:01:42

303

Views

Existence of unique fixed point in compact Metric space

Published on 25 Mar 2026 - 16:01

score 41 · Answer 8 · 2018-05-22 08:37:06

Why is $f\in C_0^{\infty}(a,b)$ equivalent to $\exists\epsilon>0\ :\ \forall x\in(-\infty,a+\epsilon)\cup(b-\epsilon,+\infty)$ s.t. $f(x)=0$?

score 680 · Answer 9 · 2026-03-25 15:58:39

680

Views

Prove that there is no fixed point

Published on 25 Mar 2026 - 15:58

score 46 · Answer 10 · 2018-05-22 11:18:19

46

Views

Sketch $M=\{re^{i\phi}:r\in(1,2],\phi\in[0,\pi)\}$ and give its closure $\overline{M}$. Is $M$ compact?

Published on 22 May 2018 - 11:18

score 51 · Answer 11 · 2018-05-22 11:57:05

51

Views

Does the open cover of a compact always contain an r-neighborhood of the compact

Published on 22 May 2018 - 11:57

score 107 · Answer 12 · 2018-05-22 12:36:26

107

Views

Let $K\subseteq\mathbb{C}$ be compact and non-empty. Show there exists a $z\in K$ such that $|z|=\inf\{|w|:w\in K\}$.

Published on 22 May 2018 - 12:36

score 182 · Answer 13 · 2018-05-22 14:20:17

182

Views

$A$ and $B$ closed in $\Bbb R^2$ but neither is compact

Published on 22 May 2018 - 14:20

score 1.5k · Answer 14 · 2018-05-23 11:06:22

1.5k

Views

Does unit sphere $S$ homeomorphic to $[0,1]$

Published on 23 May 2018 - 11:06

score 744 · Answer 15 · 2018-05-23 14:50:12

744

Views

An example of a compact topological space which is not the continuous image of a compact Hausdorff space?

Published on 23 May 2018 - 14:50

List Question

Proving sequence of half isometries on a compact has converging subsequence to fixed point

Open subset of locally compact non Hausdorff space which is not locally compact.

For which n differential operator $C^{(n)}[0, 1] \rightarrow C[0,1]$ is compact

Prove that $\mathbb{Z}^+$ is not compact with the arithmetic progression topology

Question about different topologies on spaces of continuous functions.

How to prove that following set is not locally compact.

Existence of unique fixed point in compact Metric space

Why is $f\in C_0^{\infty}(a,b)$ equivalent to $\exists\epsilon>0\ :\ \forall x\in(-\infty,a+\epsilon)\cup(b-\epsilon,+\infty)$ s.t. $f(x)=0$?

Prove that there is no fixed point

Sketch $M=\{re^{i\phi}:r\in(1,2],\phi\in[0,\pi)\}$ and give its closure $\overline{M}$. Is $M$ compact?

Does the open cover of a compact always contain an r-neighborhood of the compact

Let $K\subseteq\mathbb{C}$ be compact and non-empty. Show there exists a $z\in K$ such that $|z|=\inf\{|w|:w\in K\}$.

$A$ and $B$ closed in $\Bbb R^2$ but neither is compact

Does unit sphere $S$ homeomorphic to $[0,1]$

An example of a compact topological space which is not the continuous image of a compact Hausdorff space?

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