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Question about nowhere dense condition in Baire category theorem application

score 378 · Answer 1 · 2017-09-01 11:26:03

378

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Question about nowhere dense condition in Baire category theorem application

Published on 01 Sep 2017 - 11:26

score 504 · Answer 2 · 2017-09-01 22:08:37

504

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Prove $\mathbb{R}$ is not a countable, disjoint union of proper closed subsets. How about $\mathbb{R}^n$?

Published on 01 Sep 2017 - 22:08

score 580 · Answer 3 · 2017-09-08 17:36:18

580

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Is a function with a dense set of points of continuity of Baire Class 1?

Published on 08 Sep 2017 - 17:36

score 511 · Answer 4 · 2017-09-13 08:40:11

511

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Sets that are generic but not of second category and vice versa

Published on 13 Sep 2017 - 8:40

score 20 · Answer 5 · 2017-09-14 22:00:21

20

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First category $ \cup_{n}\cap_{m}\cup_{k}A_{n,m,k} $

Published on 14 Sep 2017 - 22:00

score 1.2k · Answer 6 · 2017-09-15 19:42:44

1.2k

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Is $\mathbb R$ of second category in itself?

Published on 15 Sep 2017 - 19:42

score 1k · Answer 7 · 2026-03-29 05:11:00

1k

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A proof using Baire Category Theorem

Published on 29 Mar 2026 - 5:11

score 1.4k · Answer 8 · 2017-10-16 21:37:34

1.4k

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Proving that every forward orbit is dense for a homeomorphism on the torus.

Published on 16 Oct 2017 - 21:37

score 206 · Answer 9 · 2017-10-20 06:57:10

206

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If $A$ is nowhere dense, then $Int(\overline{A})=\emptyset.$

Published on 20 Oct 2017 - 6:57

score 41 · Answer 10 · 2017-10-22 06:07:07

41

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$\bigcup_{k\in \mathbb{N}} F_k^\circ$ is dense in $\mathbb{R}$

Published on 22 Oct 2017 - 6:07

score 504 · Answer 11 · 2017-10-23 12:20:02

504

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Proof explanation of Borel Theorem on $\mathbb{R}$

Published on 23 Oct 2017 - 12:20

score 1.1k · Answer 12 · 2017-10-29 09:14:19

1.1k

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intuition of decomposition of $\mathbb{R}$ into disjoint union of first category and null set

Published on 29 Oct 2017 - 9:14

score 272 · Answer 13 · 2017-11-01 00:28:30

272

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Variant of Baire-Osgood Theorem

Published on 01 Nov 2017 - 0:28

score 130 · Answer 14 · 2017-11-05 03:49:52

130

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Are absolutely convergent series "many" or "few" compared to conditionally convergent series?

Published on 05 Nov 2017 - 3:49

score 74 · Answer 15 · 2017-11-06 04:43:08

74

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Baire application to sequence of functions

Published on 06 Nov 2017 - 4:43

List Question

Question about nowhere dense condition in Baire category theorem application

Prove $\mathbb{R}$ is not a countable, disjoint union of proper closed subsets. How about $\mathbb{R}^n$?

Is a function with a dense set of points of continuity of Baire Class 1?

Sets that are generic but not of second category and vice versa

First category $ \cup_{n}\cap_{m}\cup_{k}A_{n,m,k} $

Is $\mathbb R$ of second category in itself?

A proof using Baire Category Theorem

Proving that every forward orbit is dense for a homeomorphism on the torus.

If $A$ is nowhere dense, then $Int(\overline{A})=\emptyset.$

$\bigcup_{k\in \mathbb{N}} F_k^\circ$ is dense in $\mathbb{R}$

Proof explanation of Borel Theorem on $\mathbb{R}$

intuition of decomposition of $\mathbb{R}$ into disjoint union of first category and null set

Variant of Baire-Osgood Theorem

Are absolutely convergent series "many" or "few" compared to conditionally convergent series?

Baire application to sequence of functions

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