Question

A set that is bounded below possess a subsequence that converges to its infimum.

score 398 · Answer 1 · 2026-04-17 04:16:08

398

Views

A set that is bounded below possess a subsequence that converges to its infimum.

Published on 17 Apr 2026 - 4:16

score 50 · Answer 2 · 2026-04-14 08:14:10

50

Views

Concluding a proof about an equivalence of two topologies given by two different metrics.

Published on 14 Apr 2026 - 8:14

score 47 · Answer 3 · 2026-04-12 11:48:00

47

Views

Proving a metric space has sequential compactness

Published on 12 Apr 2026 - 11:48

score 262 · Answer 4 · 2026-05-10 16:34:31

262

Views

$+:X\times X\to X,(x,y)\mapsto +(x,y)=x+y$ and $\cdot:\Bbb{R}\times X\to X,(\lambda,x)\mapsto \cdot(\lambda,y)=\lambda\cdot x$ are weakly continuous

Published on 10 May 2026 - 16:34

score 1.2k · Answer 5 · 2026-05-16 15:40:47

1.2k

Views

Prob. 7 (b), Sec. 28, in Munkres' TOPOLOGY, 2nd ed: A shrinking self-map of a compact metric space has a unique fixed point

Published on 16 May 2026 - 15:40

score 36 · Answer 6 · 2026-04-17 14:10:34

36

Views

If U contains some point in $A_{\alpha'}$, and $A_{\alpha'}$ is connected, then $A_{\alpha'} \subset U$.

Published on 17 Apr 2026 - 14:10

score 885 · Answer 7 · 2026-05-10 16:05:47

885

Views

What is the link between topology and graphs, if one exists?

Published on 10 May 2026 - 16:05

score 46 · Answer 8 · 2026-04-13 15:16:44

46

Views

What our the minimal requirements on the topologies on $X$ and $Y$ such that the following statement is true?

Published on 13 Apr 2026 - 15:16

score 189 · Answer 9 · 2026-04-12 02:55:00

189

Views

Is compactness (without Hausdorff) enough to get a closed quotient map?

Published on 12 Apr 2026 - 2:55

score 72 · Answer 10 · 2026-05-10 19:45:04

72

Views

Visualization / sketch for this basic proof about subspace topology

Published on 10 May 2026 - 19:45

score 259 · Answer 11 · 2026-05-16 10:17:20

259

Views

$A$ closed, $B$ compact. $A$ and $B$ are disjoint. Prove that the distance between them is positive.

Published on 16 May 2026 - 10:17

score 61 · Answer 12 · 2026-04-29 18:20:58

61

Views

A question about showing how a product of closed sets in the product toplogy is closed .

Published on 29 Apr 2026 - 18:20

score 49 · Answer 13 · 2026-04-16 15:45:34

49

Views

Let $X=\{0,1\}$ and $\tau =\{ \emptyset , X, \{0\} \}$. Is $(x_n)=0,0,... $ convergence?

Published on 16 Apr 2026 - 15:45

score 883 · Answer 14 · 2026-04-12 14:14:19

883

Views

Proof that interval $]0,1[$ is an open set

Published on 12 Apr 2026 - 14:14

score 168 · Answer 15 · 2026-04-29 18:20:58

168

Views

a contradiction in my proof to show that T must be the discrete topology if $f:(X,T)\rightarrow (\Bbb R,T_{st})$, I dont understand .

Published on 29 Apr 2026 - 18:20

List Question

A set that is bounded below possess a subsequence that converges to its infimum.

Concluding a proof about an equivalence of two topologies given by two different metrics.

Proving a metric space has sequential compactness

$+:X\times X\to X,(x,y)\mapsto +(x,y)=x+y$ and $\cdot:\Bbb{R}\times X\to X,(\lambda,x)\mapsto \cdot(\lambda,y)=\lambda\cdot x$ are weakly continuous

Prob. 7 (b), Sec. 28, in Munkres' TOPOLOGY, 2nd ed: A shrinking self-map of a compact metric space has a unique fixed point

If U contains some point in $A_{\alpha'}$, and $A_{\alpha'}$ is connected, then $A_{\alpha'} \subset U$.

What is the link between topology and graphs, if one exists?

What our the minimal requirements on the topologies on $X$ and $Y$ such that the following statement is true?

Is compactness (without Hausdorff) enough to get a closed quotient map?

Visualization / sketch for this basic proof about subspace topology

$A$ closed, $B$ compact. $A$ and $B$ are disjoint. Prove that the distance between them is positive.

A question about showing how a product of closed sets in the product toplogy is closed .

Let $X=\{0,1\}$ and $\tau =\{ \emptyset , X, \{0\} \}$. Is $(x_n)=0,0,... $ convergence?

Proof that interval $]0,1[$ is an open set

a contradiction in my proof to show that T must be the discrete topology if $f:(X,T)\rightarrow (\Bbb R,T_{st})$, I dont understand .

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