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 868 · Answer 1 · 2026-03-24 02:39:24

868

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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 24 Mar 2026 - 2:39

score 171 · Answer 2 · 2026-03-25 09:51:02

171

Views

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

Published on 25 Mar 2026 - 9:51

score 445 · Answer 3 · 2019-06-19 01:08:07

445

Views

Use of Axiom of Choice in Baire Category Theorem

Published on 19 Jun 2019 - 1:08

score 219 · Answer 4 · 2019-06-24 14:47:09

219

Views

Every set of second category is everywhere dense

Published on 24 Jun 2019 - 14:47

score 204 · Answer 5 · 2026-03-25 16:01:35

204

Views

Elementary example of Baire spaces whose product is not Baire

Published on 25 Mar 2026 - 16:01

score 60 · Answer 6 · 2019-06-26 11:31:49

60

Views

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

Published on 26 Jun 2019 - 11:31

score 1.4k · Answer 7 · 2019-07-04 12:56:34

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 04 Jul 2019 - 12:56

score 66 · Answer 8 · 2019-07-17 09:18:05

66

Views

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

Published on 17 Jul 2019 - 9:18

score 222 · Answer 9 · 2019-08-07 18:52:17

222

Views

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

Published on 07 Aug 2019 - 18:52

score 57 · Answer 10 · 2019-08-07 20:58:48

57

Views

How can it can be countable intersection?

Published on 07 Aug 2019 - 20:58

score 105 · Answer 11 · 2019-08-14 13:14:38

105

Views

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

Published on 14 Aug 2019 - 13:14

score 43 · Answer 12 · 2019-08-23 16:51:49

43

Views

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

Published on 23 Aug 2019 - 16:51

score 106 · Answer 13 · 2019-08-26 01:10:02

106

Views

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

Published on 26 Aug 2019 - 1:10

score 107 · Answer 14 · 2019-08-31 05:03:07

107

Views

Category definition for Baire's Theorem

Published on 31 Aug 2019 - 5:03

score 73 · Answer 15 · 2019-09-18 04:48:33

73

Views

nowhere dense set on circle

Published on 18 Sep 2019 - 4:48

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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