Question

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

score 42 · Answer 1 · 2026-05-11 02:52:27

42

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

Published on 11 May 2026 - 2:52

score 231 · Answer 2 · 2026-04-09 15:10:56

231

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

Published on 09 Apr 2026 - 15:10

score 559 · Answer 3 · 2026-05-10 18:03:33

559

Views

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

Published on 10 May 2026 - 18:03

score 424 · Answer 4 · 2026-04-12 21:23:42

424

Views

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

Published on 12 Apr 2026 - 21:23

score 63 · Answer 5 · 2026-05-14 18:28:30

63

Views

Question about different topologies on spaces of continuous functions.

Published on 14 May 2026 - 18:28

score 47 · Answer 6 · 2026-05-14 12:52:28

47

Views

How to prove that following set is not locally compact.

Published on 14 May 2026 - 12:52

score 306 · Answer 7 · 2026-05-11 00:47:14

306

Views

Existence of unique fixed point in compact Metric space

Published on 11 May 2026 - 0:47

score 44 · Answer 8 · 2026-04-16 19:27:29

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 683 · Answer 9 · 2026-05-11 01:48:52

683

Views

Prove that there is no fixed point

Published on 11 May 2026 - 1:48

score 49 · Answer 10 · 2026-04-17 14:50:22

49

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 17 Apr 2026 - 14:50

score 54 · Answer 11 · 2026-04-12 13:09:48

54

Views

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

Published on 12 Apr 2026 - 13:09

score 110 · Answer 12 · 2026-04-13 23:34:44

110

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 13 Apr 2026 - 23:34

score 185 · Answer 13 · 2026-04-14 11:43:08

185

Views

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

Published on 14 Apr 2026 - 11:43

score 1.5k · Answer 14 · 2026-04-11 01:11:08

1.5k

Views

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

Published on 11 Apr 2026 - 1:11

score 747 · Answer 15 · 2026-04-09 17:32:13

747

Views

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

Published on 09 Apr 2026 - 17:32

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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