Question

Product topology on $R^\omega$ and Banach Spaces

score 368 · Answer 1 · 2026-03-27 02:07:11

368

Views

Product topology on $R^\omega$ and Banach Spaces

Published on 27 Mar 2026 - 2:07

score 22 · Answer 2 · 2018-03-10 13:59:25

Question about denseness in the topology $\mathcal{T}:= \{\emptyset\}\cup\{A \mid |X \setminus A| \leq |\mathbb{N}|\}$

score 254 · Answer 3 · 2018-03-10 14:52:09

254

Views

Are every maximal connected(resp. path connected) sets, components(resp. path components)?

Published on 10 Mar 2018 - 14:52

score 289 · Answer 4 · 2026-03-26 01:23:37

289

Views

Any open neighborhood of a boundary point contains an interior point and an exterior point.

Published on 26 Mar 2026 - 1:23

score 408 · Answer 5 · 2026-03-26 08:00:41

408

Views

A sequence $\{x_n\}$ is convergent in $\prod X_\alpha$ iff the projection sequence $\{\pi_\alpha(x_n)\}$ converges in $X_\alpha$ for any $\alpha$

Published on 26 Mar 2026 - 8:00

score 191 · Answer 6 · 2026-03-25 01:14:53

191

Views

Logarithmic spiral is an embedding

Published on 25 Mar 2026 - 1:14

score 433 · Answer 7 · 2026-03-20 08:40:14

433

Views

If $\mathcal{F}$ is a filter on a set $X$, then there exists an ultrafilter $\mathcal{U}$ such that $\mathcal{F} \subseteq \mathcal{U}$

Published on 20 Mar 2026 - 8:40

score 873 · Answer 8 · 2018-03-10 18:52:36

873

Views

Must a surjective continuous map on a compact space into itself be injective?

Published on 10 Mar 2018 - 18:52

score 97 · Answer 9 · 2026-03-27 18:19:23

97

Views

is compactness equivalent to limit point compactness?

Published on 27 Mar 2026 - 18:19

score 52 · Answer 10 · 2026-03-26 04:42:19

52

Views

How to show $\hat{x}\in X^{**}$ without using $(X^,wk^)^*\subseteq X^{**}$?

Published on 26 Mar 2026 - 4:42

score 294 · Answer 11 · 2026-03-19 16:35:48

294

Views

Let $X$ be a finite set. Prove that every ultrafilter is a point filter.

Published on 19 Mar 2026 - 16:35

score 3.7k · Answer 12 · 2026-03-30 07:00:16

3.7k

Views

Definition of a limit point in a metric space

Published on 30 Mar 2026 - 7:00

score 974 · Answer 13 · 2018-03-10 21:25:06

974

Views

Quotient of the torus being homeomorphic to Mobius strip?

Published on 10 Mar 2018 - 21:25

score 154 · Answer 14 · 2026-03-23 01:46:37

154

Views

Definition of a (topologically) continuous functor

Published on 23 Mar 2026 - 1:46

score 591 · Answer 15 · 2018-03-11 03:26:19

591

Views

Does $B \subset \overline{A}$ always mean $A$ is dense in $B$?

Published on 11 Mar 2018 - 3:26

List Question

Product topology on $R^\omega$ and Banach Spaces

Question about denseness in the topology $\mathcal{T}:= \{\emptyset\}\cup\{A \mid |X \setminus A| \leq |\mathbb{N}|\}$

Are every maximal connected(resp. path connected) sets, components(resp. path components)?

Any open neighborhood of a boundary point contains an interior point and an exterior point.

A sequence $\{x_n\}$ is convergent in $\prod X_\alpha$ iff the projection sequence $\{\pi_\alpha(x_n)\}$ converges in $X_\alpha$ for any $\alpha$

Logarithmic spiral is an embedding

If $\mathcal{F}$ is a filter on a set $X$, then there exists an ultrafilter $\mathcal{U}$ such that $\mathcal{F} \subseteq \mathcal{U}$

Must a surjective continuous map on a compact space into itself be injective?

is compactness equivalent to limit point compactness?

How to show $\hat{x}\in X^{**}$ without using $(X^,wk^)^*\subseteq X^{**}$?

Let $X$ be a finite set. Prove that every ultrafilter is a point filter.

Definition of a limit point in a metric space

Quotient of the torus being homeomorphic to Mobius strip?

Definition of a (topologically) continuous functor

Does $B \subset \overline{A}$ always mean $A$ is dense in $B$?

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