List questions from baire-category

Published on 01 Jun 2013 - 14:12

1.2k

Views

Can a sequence of functions have infinity as limit exactly at rationals?

Published on 18 Jul 2013 - 3:22

112

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$X$ is a complete metric space, $Y$ is compact. $X \times Y$ is Baire?

Published on 23 Jul 2013 - 1:14

1.5k

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Examples of closed subspaces of Baire spaces that fail to be Baire?

Published on 25 Jul 2013 - 0:36

2.6k

Views

Diophantine number has full measure but is meager

Published on 06 Aug 2013 - 8:02

257

Views

$X$ a separable metric space with no isolated points. If $G \subset X$ is a countable dense $G_{\delta}$ subset of $X$, why is $X$ meager?

Published on 21 Aug 2013 - 18:01

1k

Views

Is this Baire theorem a special case of Baire category theorem?

Published on 08 Sep 2013 - 12:21

57

Views

In a Baire space $X$, if an open set meets a nonmeager set, is the intersection nonmeager?

Published on 11 Sep 2013 - 12:53

469

Views

Can a locally compact group with closed singleton be countable but not discrete?

Published on 26 Mar 2026 - 19:17

212

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Measure spaces are proper subsets

Published on 02 Oct 2013 - 14:23

427

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$L_2$ is of first category in $L_1$ (Rudin Excercise 2.4b)

Published on 10 Oct 2013 - 14:01

35

Views

Confusion about this assertion

Published on 11 Oct 2013 - 21:03

1.5k

Views

Any example of open set of first category?

Published on 19 Oct 2013 - 1:56

161

Views

Genericity and category

Published on 25 Mar 2026 - 23:34

148

Views

Baire Category Theorem in a Smooth Manifold

Published on 30 Oct 2013 - 21:43

List Question

Are function spaces Baire?

Can a sequence of functions have infinity as limit exactly at rationals?

$X$ is a complete metric space, $Y$ is compact. $X \times Y$ is Baire?

Examples of closed subspaces of Baire spaces that fail to be Baire?

Diophantine number has full measure but is meager

$X$ a separable metric space with no isolated points. If $G \subset X$ is a countable dense $G_{\delta}$ subset of $X$, why is $X$ meager?

Is this Baire theorem a special case of Baire category theorem?

In a Baire space $X$, if an open set meets a nonmeager set, is the intersection nonmeager?

Can a locally compact group with closed singleton be countable but not discrete?

Measure spaces are proper subsets

$L_2$ is of first category in $L_1$ (Rudin Excercise 2.4b)

Confusion about this assertion

Any example of open set of first category?

Genericity and category

Baire Category Theorem in a Smooth Manifold

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