Question

Find a sequence of functions $\{g_n\}$ in $C([0,1])$ so that $\overline{\{g_n\}}$ is compact, but $g_n$ does not converge uniformly.

score 141 · Answer 1 · 2026-04-17 06:24:43

141

Views

Find a sequence of functions $\{g_n\}$ in $C([0,1])$ so that $\overline{\{g_n\}}$ is compact, but $g_n$ does not converge uniformly.

Published on 17 Apr 2026 - 6:24

score 1k · Answer 2 · 2026-04-13 08:12:45

1k

Views

Uniform convergence with supremum norm

Published on 13 Apr 2026 - 8:12

score 186 · Answer 3 · 2026-04-16 13:44:47

186

Views

$\ell^2$-convergence of convolution square root implies uniform convergence

Published on 16 Apr 2026 - 13:44

score 99 · Answer 4 · 2026-04-15 11:16:05

99

Views

On uniform convergence

Published on 15 Apr 2026 - 11:16

score 31 · Answer 5 · 2026-04-17 00:27:24

31

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Counterexample of $\lim_{x\rightarrow \infty}f(x,t(x))\neq 1$ where $\lim_{x\rightarrow \infty }t(x)=2$.

Published on 17 Apr 2026 - 0:27

score 118 · Answer 6 · 2026-04-11 22:31:11

118

Views

Explanation for why $f(x) = x - x^n$ does not converge uniformly?

Published on 11 Apr 2026 - 22:31

score 626 · Answer 7 · 2026-05-14 23:45:18

626

Views

Show that $f_{n}(x)=\frac{x}{1+nx^{2}}$ converges uniformly.

Published on 14 May 2026 - 23:45

score 145 · Answer 8 · 2026-04-16 06:45:08

145

Views

Show that the series $\sum \frac{\sin(n)}{1+n^{2}x^{2}}$ converges uniformly.

Published on 16 Apr 2026 - 6:45

score 713 · Answer 9 · 2026-04-12 18:50:14

713

Views

Prove that an entire sequence uniformly converges to an entire function on compact set

Published on 12 Apr 2026 - 18:50

score 81 · Answer 10 · 2026-04-11 13:37:08

81

Views

Uniform convergence of the following series:

Published on 11 Apr 2026 - 13:37

score 1.1k · Answer 11 · 2026-04-16 12:17:10

1.1k

Views

Prove that $\sum\limits_{n=1}(-1)^n\frac{x^2+n}{n^2}$ uniformly convergent on $[a,b]$

Published on 16 Apr 2026 - 12:17

score 1.1k · Answer 12 · 2026-04-11 13:16:43

1.1k

Views

If $f_n\to f$ pointwise, $f$ is continuous and $f$ is continuous, then $f_n \to f$ uniformly.

Published on 11 Apr 2026 - 13:16

score 78 · Answer 13 · 2026-04-15 07:51:56

78

Views

Is there such a theorem about uniform convergence?

Published on 15 Apr 2026 - 7:51

score 474 · Answer 14 · 2026-04-13 03:58:30

474

Views

Does $f_n$ converge uniformly?

Published on 13 Apr 2026 - 3:58

score 98 · Answer 15 · 2026-04-15 16:34:36

98

Views

Prove that $\sum_{n=0}^{\infty}\frac{x^n}{n!}$ is not uniformly convergent on $(0, +\infty)\ni x$.

Published on 15 Apr 2026 - 16:34

List Question

Find a sequence of functions $\{g_n\}$ in $C([0,1])$ so that $\overline{\{g_n\}}$ is compact, but $g_n$ does not converge uniformly.

Uniform convergence with supremum norm

$\ell^2$-convergence of convolution square root implies uniform convergence

On uniform convergence

Counterexample of $\lim_{x\rightarrow \infty}f(x,t(x))\neq 1$ where $\lim_{x\rightarrow \infty }t(x)=2$.

Explanation for why $f(x) = x - x^n$ does not converge uniformly?

Show that $f_{n}(x)=\frac{x}{1+nx^{2}}$ converges uniformly.

Show that the series $\sum \frac{\sin(n)}{1+n^{2}x^{2}}$ converges uniformly.

Prove that an entire sequence uniformly converges to an entire function on compact set

Uniform convergence of the following series:

Prove that $\sum\limits_{n=1}(-1)^n\frac{x^2+n}{n^2}$ uniformly convergent on $[a,b]$

If $f_n\to f$ pointwise, $f$ is continuous and $f$ is continuous, then $f_n \to f$ uniformly.

Is there such a theorem about uniform convergence?

Does $f_n$ converge uniformly?

Prove that $\sum_{n=0}^{\infty}\frac{x^n}{n!}$ is not uniformly convergent on $(0, +\infty)\ni x$.

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