Question

Prove $∪_{k=1}^N[x_k − δ, x_k + δ] ⊃ [0, 1]$

score 37 · Answer 1 · 2026-02-24 03:50:38

37

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Prove $∪_{k=1}^N[x_k − δ, x_k + δ] ⊃ [0, 1]$

Published on 24 Feb 2026 - 3:50

score 113 · Answer 2 · 2020-03-28 02:36:47

113

Views

Prove that $f_n$ converges uniformly to some continuous function $f(x)$ defined in R.

Published on 28 Mar 2020 - 2:36

score 195 · Answer 3 · 2020-03-28 16:40:11

195

Views

Question regarding sequence of continuous functions

Published on 28 Mar 2020 - 16:40

score 49 · Answer 4 · 2020-03-31 16:04:43

49

Views

Series $\sum \limits_{k=1}^{\infty}f_{n}(x)$ converges uniformly, but $\sum \limits_{k=1}^{\infty}|f_{n}(x)|$ converges only pointwise

Published on 31 Mar 2020 - 16:04

score 513 · Answer 5 · 2020-04-05 12:01:08

513

Views

Is $(C^1[0,1],\|\cdot\|)$ with $\|f\|:=|f(0)|+\sup_{0\le{t\le{1}}}{|f'(t)|}$ a Banach space?

Published on 05 Apr 2020 - 12:01

score 260 · Answer 6 · 2020-04-06 01:54:59

260

Views

Show that the closed unit ball in $L^2[a,b]$ is not sequentially compact.

Published on 06 Apr 2020 - 1:54

score 42 · Answer 7 · 2020-04-07 01:33:33

42

Views

How to prove this limit exists almost everywhere, in a space of sequences?

Published on 07 Apr 2020 - 1:33

score 97 · Answer 8 · 2020-04-07 11:35:34

97

Views

Limit of continuous function of sequence of $L^2$ functions

Published on 07 Apr 2020 - 11:35

score 94 · Answer 9 · 2020-04-08 06:07:02

94

Views

Points of continuity of a sequence of almost everywhere continuous functions

Published on 08 Apr 2020 - 6:07

score 88 · Answer 10 · 2020-04-17 17:05:41

88

Views

Limits under integrals and uniform convergence.

Published on 17 Apr 2020 - 17:05

score 139 · Answer 11 · 2026-02-24 05:37:27

139

Views

Prove that there exist infinitely many subsequences of $(f_m)_{m≥1}$ which converge at every point of $E$.

Published on 24 Feb 2026 - 5:37

score 101 · Answer 12 · 2020-04-19 03:40:56

101

Views

$\{f_n\}$ converges uniformly but $\lim_{n\rightarrow\infty}f_n$ doesn't exist

Published on 19 Apr 2020 - 3:40

score 241 · Answer 13 · 2020-04-19 15:45:00

241

Views

Maclaurin series and general term for $e^{(x-2)^2}$

Published on 19 Apr 2020 - 15:45

score 104 · Answer 14 · 2020-04-20 17:34:39

104

Views

Continuous functions $f_n:[0,1]\to [0,\infty)$ such that $f_n\to 0$, $\int_0^1 f_n(x)dx\to 0$, but $\sup_nf_n$ is not in $L^1$.

Published on 20 Apr 2020 - 17:34

score 96 · Answer 15 · 2020-04-22 08:53:40

96

Views

Uniformly bounded and Convergence subsequence

Published on 22 Apr 2020 - 8:53

List Question

Prove $∪_{k=1}^N[x_k − δ, x_k + δ] ⊃ [0, 1]$

Prove that $f_n$ converges uniformly to some continuous function $f(x)$ defined in R.

Question regarding sequence of continuous functions

Series $\sum \limits_{k=1}^{\infty}f_{n}(x)$ converges uniformly, but $\sum \limits_{k=1}^{\infty}|f_{n}(x)|$ converges only pointwise

Is $(C^1[0,1],\|\cdot\|)$ with $\|f\|:=|f(0)|+\sup_{0\le{t\le{1}}}{|f'(t)|}$ a Banach space?

Show that the closed unit ball in $L^2[a,b]$ is not sequentially compact.

How to prove this limit exists almost everywhere, in a space of sequences?

Limit of continuous function of sequence of $L^2$ functions

Points of continuity of a sequence of almost everywhere continuous functions

Limits under integrals and uniform convergence.

Prove that there exist infinitely many subsequences of $(f_m)_{m≥1}$ which converge at every point of $E$.

$\{f_n\}$ converges uniformly but $\lim_{n\rightarrow\infty}f_n$ doesn't exist

Maclaurin series and general term for $e^{(x-2)^2}$

Continuous functions $f_n:[0,1]\to [0,\infty)$ such that $f_n\to 0$, $\int_0^1 f_n(x)dx\to 0$, but $\sup_nf_n$ is not in $L^1$.

Uniformly bounded and Convergence subsequence

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