List questions from baire-category

Published on 12 Apr 2017 - 15:46

43

Views

If $f$ is of Baire Class $1$, then $|f^{-1}[\{0\}]|=\mathfrak c$ or is countable.

Published on 15 Apr 2017 - 2:18

55

Views

How to show that in the space X=Q with the usual absolute value metric, the whole space is of first category in X

Published on 18 Apr 2017 - 19:10

152

Views

In a Polish space, a set is comeager if it is nonmeager in every open set?

Published on 28 Mar 2026 - 13:21

119

Views

Is the space of probability measures second category?

Published on 28 May 2017 - 16:53

184

Views

Baire class 1 function

Published on 28 May 2017 - 21:51

501

Views

Is the cardinality of an open set in a complete metric space $X$ with no isolated points equal to $|X|$?

Published on 31 May 2017 - 18:27

387

Views

An exercise on Baire Category Theorem

Published on 20 Jun 2017 - 7:23

239

Views

Normal numbers are meager

Published on 29 Jun 2017 - 10:27

65

Views

The set of $e \in \{0,1\}^{\mathbf{N}}$ such that $e_1+\cdots+e_n\neq o(n)$

Published on 30 Jun 2017 - 16:13

120

Views

Countable and dense Baire subsets

Published on 25 Mar 2026 - 18:44

859

Views

Baire Category Theorem without Completeness

Published on 21 Jul 2017 - 14:41

35

Views

Countable intersection of Baire subspaces

Published on 25 Jul 2017 - 1:56

355

Views

Is every Baire space Cech-complete?

Published on 13 Aug 2017 - 18:40

327

Views

When the intersection of two sets of second category is of second category?

Published on 25 Aug 2017 - 1:43

List Question

A nowhere dense subset of $\mathbb{R}$ is countable

If $f$ is of Baire Class $1$, then $|f^{-1}[\{0\}]|=\mathfrak c$ or is countable.

How to show that in the space X=Q with the usual absolute value metric, the whole space is of first category in X

In a Polish space, a set is comeager if it is nonmeager in every open set?

Is the space of probability measures second category?

Baire class 1 function

Is the cardinality of an open set in a complete metric space $X$ with no isolated points equal to $|X|$?

An exercise on Baire Category Theorem

Normal numbers are meager

The set of $e \in \{0,1\}^{\mathbf{N}}$ such that $e_1+\cdots+e_n\neq o(n)$

Countable and dense Baire subsets

Baire Category Theorem without Completeness

Countable intersection of Baire subspaces

Is every Baire space Cech-complete?

When the intersection of two sets of second category is of second category?

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