Question

If $(X, \tau)$ is a Baire space, then $X \times [0,1]_{std}$ is a Baire space

score 40 · Answer 1 · 2023-07-21 20:57:13

40

Views

If $(X, \tau)$ is a Baire space, then $X \times [0,1]_{std}$ is a Baire space

Published on 21 Jul 2023 - 20:57

score 61 · Answer 2 · 2023-08-08 11:05:23

61

Views

f(tn) converges -> f(t) converges

Published on 08 Aug 2023 - 11:05

score 40 · Answer 3 · 2026-03-27 14:51:42

40

Views

Is there a metric $d$ such that $(\mathbb{F}[x], d)$ is complete?

Published on 27 Mar 2026 - 14:51

score 42 · Answer 4 · 2026-03-25 17:37:37

42

Views

Nowhere Dense Set and Corollary to Baire's Theorem

Published on 25 Mar 2026 - 17:37

score 551 · Answer 5 · 2023-09-16 20:27:11

551

Views

Prove that $[0,1]$ is not a disjoint union of a countable family of closed sets

Published on 16 Sep 2023 - 20:27

score 60 · Answer 6 · 2023-10-13 19:08:56

60

Views

Understanding the Proof of the Smale Sard Theorem

Published on 13 Oct 2023 - 19:08

score 93 · Answer 7 · 2023-10-23 10:33:14

93

Views

Essentially discontinuous on a dense subset of $\mathbb{R}$, but continuous on the complement which is also dense

Published on 23 Oct 2023 - 10:33

score 26 · Answer 8 · 2023-10-25 15:36:43

26

Views

Convex lsc function on a Banach space and Baire's theorem

Published on 25 Oct 2023 - 15:36

score 48 · Answer 9 · 2023-11-10 10:22:30

48

Views

Are the irrationals Gδ because they are uncountable?

Published on 10 Nov 2023 - 10:22

score 22 · Answer 10 · 2026-03-25 19:11:14

22

Views

Showing a certain dense subset of $\mathcal{C}^1([0,1]^2,\mathbb{R}^4)$ is residual.

Published on 25 Mar 2026 - 19:11

score 23 · Answer 11 · 2026-03-26 22:54:12

23

Views

Ergodic transformations form a $G_\delta$ set in the weak topology of the automorphism group.

Published on 26 Mar 2026 - 22:54

score 141 · Answer 12 · 2023-12-13 13:37:58

141

Views

$\lim\limits_{n\rightarrow\infty}f(2^{n}x)=0$ implies$\lim\limits_{x\rightarrow\infty}f(x)=0?$

Published on 13 Dec 2023 - 13:37

score 42 · Answer 13 · 2024-01-02 11:26:26

42

Views

Exercise about repeated primitives

Published on 02 Jan 2024 - 11:26

score 112 · Answer 14 · 2026-02-23 04:42:58

112

Views

Must a subset of the real line that is comprised entirely of condensation points be a Baire space?

Published on 23 Feb 2026 - 4:42

score 70 · Answer 15 · 2024-02-01 03:14:19

70

Views

Graph of a monotone function is nowhere dense.

Published on 01 Feb 2024 - 3:14

List Question

If $(X, \tau)$ is a Baire space, then $X \times [0,1]_{std}$ is a Baire space

f(tn) converges -> f(t) converges

Is there a metric $d$ such that $(\mathbb{F}[x], d)$ is complete?

Nowhere Dense Set and Corollary to Baire's Theorem

Prove that $[0,1]$ is not a disjoint union of a countable family of closed sets

Understanding the Proof of the Smale Sard Theorem

Essentially discontinuous on a dense subset of $\mathbb{R}$, but continuous on the complement which is also dense

Convex lsc function on a Banach space and Baire's theorem

Are the irrationals Gδ because they are uncountable?

Showing a certain dense subset of $\mathcal{C}^1([0,1]^2,\mathbb{R}^4)$ is residual.

Ergodic transformations form a $G_\delta$ set in the weak topology of the automorphism group.

$\lim\limits_{n\rightarrow\infty}f(2^{n}x)=0$ implies$\lim\limits_{x\rightarrow\infty}f(x)=0?$

Exercise about repeated primitives

Must a subset of the real line that is comprised entirely of condensation points be a Baire space?

Graph of a monotone function is nowhere dense.

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