Question

Which of the following are true in topological spaces?

score 692 · Answer 1 · 2026-04-12 11:57:14

692

Views

Which of the following are true in topological spaces?

Published on 12 Apr 2026 - 11:57

score 218 · Answer 2 · 2026-04-17 13:28:31

218

Views

Let $f$ be a function from a metric space to a metric space. Prove that $f$ is continuous i.f.f it sends convergent sequences into convergent seq.

Published on 17 Apr 2026 - 13:28

score 1.3k · Answer 3 · 2026-04-14 13:15:51

1.3k

Views

Number of connected components Invariant

Published on 14 Apr 2026 - 13:15

score 336 · Answer 4 · 2026-04-14 09:35:51

336

Views

Is there an explicit function from the quotient space of an annulus to a torus?

Published on 14 Apr 2026 - 9:35

score 32 · Answer 5 · 2026-04-11 13:50:55

32

Views

How do I use the uniform property of quotient spaces to establish a homeomorphism.

Published on 11 Apr 2026 - 13:50

score 178 · Answer 6 · 2026-05-10 19:06:27

178

Views

Simplicial set associated to a topological space

Published on 10 May 2026 - 19:06

score 62 · Answer 7 · 2026-04-15 05:06:47

Show the intersection of two parts of an $n$-sphere, each homeomorphic an $n$-disk have a union that's homeomorphic to an $n-1$-sphere.

score 955 · Answer 8 · 2026-04-11 13:17:29

955

Views

Quotient space homeomorphic to sphere.

Published on 11 Apr 2026 - 13:17

score 77 · Answer 9 · 2026-04-14 20:38:35

77

Views

Verification of completeness of $d_1 (x,y) = |\log x -\log y|$

Published on 14 Apr 2026 - 20:38

score 72 · Answer 10 · 2026-04-13 15:50:25

72

Views

inclusion $\Bbb R \hookrightarrow \Bbb R^2/\Bbb Z^2$ is an injective morphism but not a homeomorphism

Published on 13 Apr 2026 - 15:50

score 352 · Answer 11 · 2026-04-12 03:25:58

352

Views

Is the unitary group connected in infinite dimensions?

Published on 12 Apr 2026 - 3:25

score 180 · Answer 12 · 2026-04-13 10:46:40

180

Views

Four sheeted cover of $\mathbb{R}P^2$ wedged with circles

Published on 13 Apr 2026 - 10:46

score 122 · Answer 13 · 2026-05-16 09:10:04

122

Views

Counterexample of any infinite union of open balls is a complement of a compact set in $R^d$.

Published on 16 May 2026 - 9:10

score 826 · Answer 14 · 2026-04-11 18:38:56

826

Views

The sphere $S^n$ admits a partition of unity consisting of two functions

Published on 11 Apr 2026 - 18:38

score 505 · Answer 15 · 2026-04-14 05:49:27

505

Views

Counterxample: A continuous closed surjective map doesn't preserve Hausdorff property

Published on 14 Apr 2026 - 5:49

List Question

Which of the following are true in topological spaces?

Let $f$ be a function from a metric space to a metric space. Prove that $f$ is continuous i.f.f it sends convergent sequences into convergent seq.

Number of connected components Invariant

Is there an explicit function from the quotient space of an annulus to a torus?

How do I use the uniform property of quotient spaces to establish a homeomorphism.

Simplicial set associated to a topological space

Show the intersection of two parts of an $n$-sphere, each homeomorphic an $n$-disk have a union that's homeomorphic to an $n-1$-sphere.

Quotient space homeomorphic to sphere.

Verification of completeness of $d_1 (x,y) = |\log x -\log y|$

inclusion $\Bbb R \hookrightarrow \Bbb R^2/\Bbb Z^2$ is an injective morphism but not a homeomorphism

Is the unitary group connected in infinite dimensions?

Four sheeted cover of $\mathbb{R}P^2$ wedged with circles

Counterexample of any infinite union of open balls is a complement of a compact set in $R^d$.

The sphere $S^n$ admits a partition of unity consisting of two functions

Counterxample: A continuous closed surjective map doesn't preserve Hausdorff property

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