Question

Having trouble showing existence of pointwise convergent subsequence of a sequence of real-valued pointwise bounded functions on a countable set.

score 585 · Answer 1 · 2026-02-23 14:13:13

585

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Having trouble showing existence of pointwise convergent subsequence of a sequence of real-valued pointwise bounded functions on a countable set.

Published on 23 Feb 2026 - 14:13

score 480 · Answer 2 · 2026-02-23 14:11:23

480

Views

Sequence of functions that fails certain conditions of Arzela-Ascoli theorem

Published on 23 Feb 2026 - 14:11

score 1.4k · Answer 3 · 2026-02-23 14:09:43

1.4k

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Show that a sequence of uniformly bounded continuous functions with Lipschitz condition is pre-compact in the space of bounded continuous functions

Published on 23 Feb 2026 - 14:09

score 968 · Answer 4 · 2016-04-21 19:09:54

968

Views

Equicontinuous problem: supremum of equicontinuous functions

Published on 21 Apr 2016 - 19:09

score 1.5k · Answer 5 · 2026-02-23 14:11:13

1.5k

Views

Show the converse of the Arzela-Ascoli theorem

Published on 23 Feb 2026 - 14:11

score 135 · Answer 6 · 2016-06-21 01:52:07

135

Views

Uniform convergence of a equicontinuous sequence of functions

Published on 21 Jun 2016 - 1:52

score 131 · Answer 7 · 2016-06-26 18:29:44

131

Views

Equivalent definition of continuity, unif.continuity, equicontinuity, etc

Published on 26 Jun 2016 - 18:29

score 1.2k · Answer 8 · 2013-05-25 15:47:52

1.2k

Views

Does pointwise equicontinuous and uniformly equicontinuous implies compactness?

Published on 25 May 2013 - 15:47

score 225 · Answer 9 · 2017-05-05 18:01:08

225

Views

Equicontinuity of $\{f^n\}$ for a continuous $f:X\rightarrow X$

Published on 05 May 2017 - 18:01

score 675 · Answer 10 · 2026-02-23 14:12:36

675

Views

A subset , of the space of all continuous real valued functions on a locally compact Hausdorff space ," vanishing at infinity" , with compact closure

Published on 23 Feb 2026 - 14:12

score 570 · Answer 11 · 2017-05-18 00:59:13

570

Views

If a family of functions has an unbounded derivative, is it necessarily not uniformly equicontinuous?

Published on 18 May 2017 - 0:59

score 1k · Answer 12 · 2017-07-02 05:25:45

1k

Views

Equicontinuous sequence of functions that converges pointwise in a dense subset of its domain, converges in the whole domain.

Published on 02 Jul 2017 - 5:25

score 705 · Answer 13 · 2017-09-24 22:14:38

705

Views

equicontinuous with compactness imply uniformly equicontinuous

Published on 24 Sep 2017 - 22:14

score 1.6k · Answer 14 · 2017-09-28 00:38:55

1.6k

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$f_n(t)=f(nt)$ for $n=1,2,3,...,$ and $\{f_n\}$ is equicontinuous on $[0,1]$. What conclusion can you draw about $f$?

Published on 28 Sep 2017 - 0:38

score 252 · Answer 15 · 2017-09-28 02:35:36

252

Views

Questions related to $\{f_n\}$ is equicontinuous on $[0,1]$. Then $f$ is constant.

Published on 28 Sep 2017 - 2:35

List Question

Having trouble showing existence of pointwise convergent subsequence of a sequence of real-valued pointwise bounded functions on a countable set.

Sequence of functions that fails certain conditions of Arzela-Ascoli theorem

Show that a sequence of uniformly bounded continuous functions with Lipschitz condition is pre-compact in the space of bounded continuous functions

Equicontinuous problem: supremum of equicontinuous functions

Show the converse of the Arzela-Ascoli theorem

Uniform convergence of a equicontinuous sequence of functions

Equivalent definition of continuity, unif.continuity, equicontinuity, etc

Does pointwise equicontinuous and uniformly equicontinuous implies compactness?

Equicontinuity of $\{f^n\}$ for a continuous $f:X\rightarrow X$

A subset , of the space of all continuous real valued functions on a locally compact Hausdorff space ," vanishing at infinity" , with compact closure

If a family of functions has an unbounded derivative, is it necessarily not uniformly equicontinuous?

Equicontinuous sequence of functions that converges pointwise in a dense subset of its domain, converges in the whole domain.

equicontinuous with compactness imply uniformly equicontinuous

$f_n(t)=f(nt)$ for $n=1,2,3,...,$ and $\{f_n\}$ is equicontinuous on $[0,1]$. What conclusion can you draw about $f$?

Questions related to $\{f_n\}$ is equicontinuous on $[0,1]$. Then $f$ is constant.

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