Question

Let $X$ be a complete metric space. $E$ is a non empty open set in $X$ Then is $E$ a first category set or second category set.

score 883 · Answer 1 · 2026-04-29 12:55:31

883

Views

Let $X$ be a complete metric space. $E$ is a non empty open set in $X$ Then is $E$ a first category set or second category set.

Published on 29 Apr 2026 - 12:55

score 177 · Answer 2 · 2026-04-29 12:56:04

177

Views

How to show that $\mathbb{N}$ is a Baire space

Published on 29 Apr 2026 - 12:56

score 448 · Answer 3 · 2026-04-17 15:25:57

448

Views

Use of Axiom of Choice in Baire Category Theorem

Published on 17 Apr 2026 - 15:25

score 222 · Answer 4 · 2026-04-15 10:48:27

222

Views

Every set of second category is everywhere dense

Published on 15 Apr 2026 - 10:48

score 206 · Answer 5 · 2026-04-10 09:09:27

206

Views

Elementary example of Baire spaces whose product is not Baire

Published on 10 Apr 2026 - 9:09

score 63 · Answer 6 · 2026-04-15 04:47:46

63

Views

Density after removing a meagre subset from a non-empty $G_{\delta}$ subset.

Published on 15 Apr 2026 - 4:47

score 1.4k · Answer 7 · 2026-04-14 21:19:02

1.4k

Views

$A \subset X$ is nowhere dense in $X$ IFF each non-empty open set in $X$ contains an open ball whose closure is disjoint from $A$.

Published on 14 Apr 2026 - 21:19

score 69 · Answer 8 · 2026-04-15 22:52:26

69

Views

Given subset $A$ and $ A_x = \{y : (x,y) \in A\} $, Are the following equivalent

Published on 15 Apr 2026 - 22:52

score 225 · Answer 9 · 2026-04-15 23:03:42

225

Views

Yes/No : Is irrational number $(\mathbb{Q}^c$ ) are baires space?

Published on 15 Apr 2026 - 23:03

score 60 · Answer 10 · 2026-04-11 19:47:24

60

Views

How can it can be countable intersection?

Published on 11 Apr 2026 - 19:47

score 108 · Answer 11 · 2026-04-14 04:07:48

108

Views

Why is no AOC needed when proving Baire's theorem for a separable complete metric space?

Published on 14 Apr 2026 - 4:07

score 46 · Answer 12 · 2026-04-14 00:09:04

46

Views

Does their exist a countable $G_\delta$ set in $\Bbb{R}$ with usual metric.

Published on 14 Apr 2026 - 0:09

score 109 · Answer 13 · 2026-04-12 22:13:55

109

Views

Points of continuity of Baire class 1 function on Cantor set?

Published on 12 Apr 2026 - 22:13

score 110 · Answer 14 · 2026-04-16 15:08:52

110

Views

Category definition for Baire's Theorem

Published on 16 Apr 2026 - 15:08

score 77 · Answer 15 · 2026-04-14 12:45:23

77

Views

nowhere dense set on circle

Published on 14 Apr 2026 - 12:45

List Question

Let $X$ be a complete metric space. $E$ is a non empty open set in $X$ Then is $E$ a first category set or second category set.

How to show that $\mathbb{N}$ is a Baire space

Use of Axiom of Choice in Baire Category Theorem

Every set of second category is everywhere dense

Elementary example of Baire spaces whose product is not Baire

Density after removing a meagre subset from a non-empty $G_{\delta}$ subset.

$A \subset X$ is nowhere dense in $X$ IFF each non-empty open set in $X$ contains an open ball whose closure is disjoint from $A$.

Given subset $A$ and $ A_x = \{y : (x,y) \in A\} $, Are the following equivalent

Yes/No : Is irrational number $(\mathbb{Q}^c$ ) are baires space?

How can it can be countable intersection?

Why is no AOC needed when proving Baire's theorem for a separable complete metric space?

Does their exist a countable $G_\delta$ set in $\Bbb{R}$ with usual metric.

Points of continuity of Baire class 1 function on Cantor set?

Category definition for Baire's Theorem

nowhere dense set on circle

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