Question

If $f$ is a continuous and non negative function such that $\sum_{n=1}^\infty f(na)$ converges $\forall a\ge0$, prove that the convergence is uniform

score 69 · Answer 1 · 2024-02-08 19:16:28

69

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If $f$ is a continuous and non negative function such that $\sum_{n=1}^\infty f(na)$ converges $\forall a\ge0$, prove that the convergence is uniform

Published on 08 Feb 2024 - 19:16

score 62 · Answer 2 · 2026-02-24 22:27:03

62

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Pointwise limit of functions on $[0,1]$

Published on 24 Feb 2026 - 22:27

score 12 · Answer 3 · 2026-03-28 02:15:37

12

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Compact subsets of Hausdorff $h$-measure $0$ has complement of first category

Published on 28 Mar 2026 - 2:15

score 81 · Answer 4 · 2026-03-29 03:17:48

81

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How is the set $C(f)\cap V$ of second category in $V$?

Published on 29 Mar 2026 - 3:17

score 1.9k · Answer 5 · 2015-01-09 16:28:18

1.9k

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$l^p$ is of first category in $l^q$ if $1 \leq p < q< \infty$

Published on 09 Jan 2015 - 16:28

score 392 · Answer 6 · 2015-01-15 15:25:43

392

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Equivalence of Forms of Baire Category Theorem

Published on 15 Jan 2015 - 15:25

score 111 · Answer 7 · 2015-01-17 20:29:25

111

Views

Infinite intersection between a arbitrary set of integers and a set of floor powers

Published on 17 Jan 2015 - 20:29

score 1.5k · Answer 8 · 2015-02-02 12:58:57

1.5k

Views

$G_{\delta}$ sets in locally compact Hausdorff or complete metric space are Baire spaces

Published on 02 Feb 2015 - 12:58

score 203 · Answer 9 · 2015-02-05 07:51:11

203

Views

If $X$ is complete, then there is no continuous and open $\,f:X \to \mathbb{Q}$

Published on 05 Feb 2015 - 7:51

score 103 · Answer 10 · 2015-02-05 11:45:07

103

Views

Question regarding the proof that every hamel basis of an infinite space is uncountable

Published on 05 Feb 2015 - 11:45

score 264 · Answer 11 · 2015-02-07 20:26:32

264

Views

Differentiable function with a set of critical points of second category.

Published on 07 Feb 2015 - 20:26

score 1k · Answer 12 · 2015-02-21 02:36:20

1k

Views

Compact Hausdorff space is of second category

Published on 21 Feb 2015 - 2:36

score 488 · Answer 13 · 2015-02-22 19:19:53

488

Views

Application of the Baire category theory

Published on 22 Feb 2015 - 19:19

score 247 · Answer 14 · 2015-02-23 00:09:30

247

Views

Implication of Baire Category Theorem

Published on 23 Feb 2015 - 0:09

score 132 · Answer 15 · 2015-02-24 18:31:21

132

Views

Non differentiable solutions to $\partial_x f + \partial_y f =0$

Published on 24 Feb 2015 - 18:31

List Question

If $f$ is a continuous and non negative function such that $\sum_{n=1}^\infty f(na)$ converges $\forall a\ge0$, prove that the convergence is uniform

Pointwise limit of functions on $[0,1]$

Compact subsets of Hausdorff $h$-measure $0$ has complement of first category

How is the set $C(f)\cap V$ of second category in $V$?

$l^p$ is of first category in $l^q$ if $1 \leq p < q< \infty$

Equivalence of Forms of Baire Category Theorem

Infinite intersection between a arbitrary set of integers and a set of floor powers

$G_{\delta}$ sets in locally compact Hausdorff or complete metric space are Baire spaces

If $X$ is complete, then there is no continuous and open $\,f:X \to \mathbb{Q}$

Question regarding the proof that every hamel basis of an infinite space is uncountable

Differentiable function with a set of critical points of second category.

Compact Hausdorff space is of second category

Application of the Baire category theory

Implication of Baire Category Theorem

Non differentiable solutions to $\partial_x f + \partial_y f =0$

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