Question

Prove that an open ball is a closed set in ultrametric space

score 337 · Answer 1 · 2026-04-02 15:05:41

337

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Prove that an open ball is a closed set in ultrametric space

Published on 02 Apr 2026 - 15:05

score 153 · Answer 2 · 2026-03-25 01:25:39

153

Views

A compact non-discrete group for any norm cannot be countable

Published on 25 Mar 2026 - 1:25

score 24 · Answer 3 · 2026-03-31 23:51:14

24

Views

Let $\phi:M\to N$. Show that $\phi:B(N,\mathbb{R})\to B(M,\mathbb{R})$ where $\phi = f(\phi)$ (contract spaces)

Published on 31 Mar 2026 - 23:51

score 115 · Answer 4 · 2026-04-02 15:03:32

115

Views

Is the set $\{A \in \mathcal{M}(n \times n; \mathbb C ): \rho(A) < 1\}$ open?

Published on 02 Apr 2026 - 15:03

score 55 · Answer 5 · 2026-04-02 15:02:40

55

Views

Proof verification: continuity of functions using open balls

Published on 02 Apr 2026 - 15:02

score 96 · Answer 6 · 2026-03-25 04:55:33

96

Views

Quotient space with finite equivalence classes

Published on 25 Mar 2026 - 4:55

score 46 · Answer 7 · 2018-05-16 02:39:01

46

Views

Need some problems on semi continuity and semi open sets

Published on 16 May 2018 - 2:39

score 264 · Answer 8 · 2026-03-26 16:09:46

264

Views

Deformation Retractions onto the Same Subspace are Homotopic via Deformation Retractions

Published on 26 Mar 2026 - 16:09

score 39 · Answer 9 · 2026-03-25 22:06:03

39

Views

Existence of Partition of Unity Proof: How to Check the Closedness of Complement Without a Covering

Published on 25 Mar 2026 - 22:06

score 120 · Answer 10 · 2026-03-25 04:54:37

120

Views

Countable quotient space

Published on 25 Mar 2026 - 4:54

score 74 · Answer 11 · 2026-03-28 06:40:55

74

Views

Does a closed subset bounded away from boundary in the subspace topology imply compactness?

Published on 28 Mar 2026 - 6:40

score 88 · Answer 12 · 2026-04-02 15:08:53

88

Views

Proof Verification:Show that sets are open or closed in $\mathbb{R}$

Published on 02 Apr 2026 - 15:08

score 1k · Answer 13 · 2026-03-28 06:48:24

1k

Views

If $K$ compact then $K$ is closed (a proof by sequences)

Published on 28 Mar 2026 - 6:48

score 53 · Answer 14 · 2026-04-01 01:14:53

53

Views

Compactness of a set of distances

Published on 01 Apr 2026 - 1:14

score 157 · Answer 15 · 2026-03-25 06:04:48

157

Views

Do abstract harmonic analysts use topological methods to solve problems or deal with Borel hierarchy?

Published on 25 Mar 2026 - 6:04

List Question

Prove that an open ball is a closed set in ultrametric space

A compact non-discrete group for any norm cannot be countable

Let $\phi:M\to N$. Show that $\phi:B(N,\mathbb{R})\to B(M,\mathbb{R})$ where $\phi = f(\phi)$ (contract spaces)

Is the set $\{A \in \mathcal{M}(n \times n; \mathbb C ): \rho(A) < 1\}$ open?

Proof verification: continuity of functions using open balls

Quotient space with finite equivalence classes

Need some problems on semi continuity and semi open sets

Deformation Retractions onto the Same Subspace are Homotopic via Deformation Retractions

Existence of Partition of Unity Proof: How to Check the Closedness of Complement Without a Covering

Countable quotient space

Does a closed subset bounded away from boundary in the subspace topology imply compactness?

Proof Verification:Show that sets are open or closed in $\mathbb{R}$

If $K$ compact then $K$ is closed (a proof by sequences)

Compactness of a set of distances

Do abstract harmonic analysts use topological methods to solve problems or deal with Borel hierarchy?

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