Question

Can a sequence of discontinuous functions converge uniformly to a discontinuous function?

score 3.8k · Answer 1 · 2018-11-26 16:49:51

3.8k

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Can a sequence of discontinuous functions converge uniformly to a discontinuous function?

Published on 26 Nov 2018 - 16:49

score 1.2k · Answer 2 · 2018-11-26 17:57:50

1.2k

Views

Uniform convergence doesn't preserve improper integrals

Published on 26 Nov 2018 - 17:57

score 49 · Answer 3 · 2018-11-26 19:59:02

49

Views

Uniform convergence of functional series $ \sum_{n=1}^{n=+\infty} \frac{\sqrt{x}}{x^2+n}\sin(\frac{n}{x}),x>0$

Published on 26 Nov 2018 - 19:59

score 170 · Answer 4 · 2026-03-23 15:11:35

170

Views

Prove $f_n \to f$ uniformly on $\mathbb{R}$

Published on 23 Mar 2026 - 15:11

score 512 · Answer 5 · 2026-02-23 08:34:01

512

Views

Proof verification - If $f$ is continuous, then $f_{n}$ is continuous in at least one $n \in \mathbb{N}$

Published on 23 Feb 2026 - 8:34

score 87 · Answer 6 · 2018-11-28 14:19:43

87

Views

Uniform convergence of $\sum_{n \to \infty}\frac{\sqrt{x}\cos nx}{n(2nx^2+1)}$

Published on 28 Nov 2018 - 14:19

score 80 · Answer 7 · 2018-11-28 22:49:43

80

Views

For a branch-defined function, analyze the uniform convergence of it and of its series

Published on 28 Nov 2018 - 22:49

score 66 · Answer 8 · 2018-11-30 00:33:24

66

Views

uniformly convergence

Published on 30 Nov 2018 - 0:33

score 1.3k · Answer 9 · 2018-12-01 03:56:24

1.3k

Views

Prove $\sum_{n=1}^{\infty} x/(1+x)^n$ is uniformly convergent for $ x \in [1,2]$

Published on 01 Dec 2018 - 3:56

score 314 · Answer 10 · 2026-02-23 08:32:40

314

Views

Find a sequence of Lipschitz continuous functions on $[0,1]$ whose uniform limit is $\sqrt{x}$.

Published on 23 Feb 2026 - 8:32

score 1.4k · Answer 11 · 2018-12-02 05:41:42

1.4k

Views

Composition of two uniformly convergent sequences of functions is uniformly convergent?

Published on 02 Dec 2018 - 5:41

score 43 · Answer 12 · 2018-12-02 11:05:42

43

Views

Show that following series converges uniformly on $[0,1]$ if and only if $α > 1$

Published on 02 Dec 2018 - 11:05

score 62 · Answer 13 · 2026-02-23 10:18:42

62

Views

Deciding convergence of a sequence of functions

Published on 23 Feb 2026 - 10:18

score 604 · Answer 14 · 2026-02-23 10:22:53

604

Views

composition of bounded uniformly convergence sequences

Published on 23 Feb 2026 - 10:22

score 996 · Answer 15 · 2026-03-25 22:30:43

996

Views

Let $Y$ be a complete metric space. Then $C^0 (X,Y)$ is complete under the uniform convergence metric.

Published on 25 Mar 2026 - 22:30

List Question

Can a sequence of discontinuous functions converge uniformly to a discontinuous function?

Uniform convergence doesn't preserve improper integrals

Uniform convergence of functional series $ \sum_{n=1}^{n=+\infty} \frac{\sqrt{x}}{x^2+n}\sin(\frac{n}{x}),x>0$

Prove $f_n \to f$ uniformly on $\mathbb{R}$

Proof verification - If $f$ is continuous, then $f_{n}$ is continuous in at least one $n \in \mathbb{N}$

Uniform convergence of $\sum_{n \to \infty}\frac{\sqrt{x}\cos nx}{n(2nx^2+1)}$

For a branch-defined function, analyze the uniform convergence of it and of its series

uniformly convergence

Prove $\sum_{n=1}^{\infty} x/(1+x)^n$ is uniformly convergent for $ x \in [1,2]$

Find a sequence of Lipschitz continuous functions on $[0,1]$ whose uniform limit is $\sqrt{x}$.

Composition of two uniformly convergent sequences of functions is uniformly convergent?

Show that following series converges uniformly on $[0,1]$ if and only if $α > 1$

Deciding convergence of a sequence of functions

composition of bounded uniformly convergence sequences

Let $Y$ be a complete metric space. Then $C^0 (X,Y)$ is complete under the uniform convergence metric.

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