Question

In a Banach space X, if $\forall f \in C(M)$, $f$ is bounded, show M is compact

score 73 · Answer 1 · 2026-03-25 11:16:22

73

Views

In a Banach space X, if $\forall f \in C(M)$, $f$ is bounded, show M is compact

Published on 25 Mar 2026 - 11:16

score 45 · Answer 2 · 2018-02-24 16:08:49

45

Views

Set in a Metrizable Space is Closed

Published on 24 Feb 2018 - 16:08

score 83 · Answer 3 · 2026-03-24 22:12:59

83

Views

Proof verification of quotient maps on Hausdorff space

Published on 24 Mar 2026 - 22:12

score 244 · Answer 4 · 2018-02-24 17:43:01

244

Views

Determine if a set is open

Published on 24 Feb 2018 - 17:43

score 99 · Answer 5 · 2018-02-24 17:48:36

99

Views

Homeomorphism between $(0,1)^{\mathbb{R}}$ and $\mathbb{R}^{\mathbb{R}}$

Published on 24 Feb 2018 - 17:48

score 488 · Answer 6 · 2026-03-25 13:34:59

488

Views

Prove that if $x,y\in X$ and $r\in\mathbb R$ are such that $f(x)<r<f(y), $ then $\exists z\in X:f(z)=r$

Published on 25 Mar 2026 - 13:34

score 346 · Answer 7 · 2018-02-25 00:37:47

346

Views

Prove that the following collection is a $\sigma$-algebra of sets

Published on 25 Feb 2018 - 0:37

score 105 · Answer 8 · 2018-02-25 01:39:43

105

Views

What collection of intervals could not be a topology?

Published on 25 Feb 2018 - 1:39

score 278 · Answer 9 · 2026-03-25 07:42:11

278

Views

Lemma 3 of the Milnor's Topology from the differentiable viewpoint.

Published on 25 Mar 2026 - 7:42

score 201 · Answer 10 · 2026-02-23 06:39:40

201

Views

The lub of the usual and co-countable topology on $\mathbb R$

Published on 23 Feb 2026 - 6:39

score 609 · Answer 11 · 2018-02-25 10:13:49

609

Views

Are the sets $\{(x, y): x^2 + y^2 < 1\}$ and $\{(x, y): 0 < x^2 + y^2 < 1\}$ homeomorphic?

Published on 25 Feb 2018 - 10:13

score 229 · Answer 12 · 2026-03-25 17:38:41

229

Views

Compact support in calculus of variations

Published on 25 Mar 2026 - 17:38

score 60 · Answer 13 · 2018-02-25 14:43:09

60

Views

Subspace characterization for not compact space

Published on 25 Feb 2018 - 14:43

score 128 · Answer 14 · 2026-03-29 04:34:47

128

Views

Hausdorff condition: existence or choice?

Published on 29 Mar 2026 - 4:34

score 581 · Answer 15 · 2018-02-25 16:05:42

581

Views

Existence of a unique topology on $X$ given closure operator

Published on 25 Feb 2018 - 16:05

List Question

In a Banach space X, if $\forall f \in C(M)$, $f$ is bounded, show M is compact

Set in a Metrizable Space is Closed

Proof verification of quotient maps on Hausdorff space

Determine if a set is open

Homeomorphism between $(0,1)^{\mathbb{R}}$ and $\mathbb{R}^{\mathbb{R}}$

Prove that if $x,y\in X$ and $r\in\mathbb R$ are such that $f(x)<r<f(y), $ then $\exists z\in X:f(z)=r$

Prove that the following collection is a $\sigma$-algebra of sets

What collection of intervals could not be a topology?

Lemma 3 of the Milnor's Topology from the differentiable viewpoint.

The lub of the usual and co-countable topology on $\mathbb R$

Are the sets $\{(x, y): x^2 + y^2 < 1\}$ and $\{(x, y): 0 < x^2 + y^2 < 1\}$ homeomorphic?

Compact support in calculus of variations

Subspace characterization for not compact space

Hausdorff condition: existence or choice?

Existence of a unique topology on $X$ given closure operator

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