Question

Show that a subset of $C(\mathbb{R})$ is compact with norm $\lVert u\rVert = \sup\lvert\frac{u(x)}{x^2 +1} \rvert$

score 67 · Answer 1 · 2026-02-23 09:00:57

67

Views

Show that a subset of $C(\mathbb{R})$ is compact with norm $\lVert u\rVert = \sup\lvert\frac{u(x)}{x^2 +1} \rvert$

Published on 23 Feb 2026 - 9:00

score 238 · Answer 2 · 2026-02-23 09:02:41

238

Views

Ascoli-Arzelà example and equicontinuity

Published on 23 Feb 2026 - 9:02

score 173 · Answer 3 · 2026-02-23 09:03:42

173

Views

Prove the relative compactness of a sequence in $L^p$

Published on 23 Feb 2026 - 9:03

score 55 · Answer 4 · 2026-02-23 09:01:08

55

Views

Why is the image under integration of a uniformly bounded subset of $C[a,b]$ necessarily compact?

Published on 23 Feb 2026 - 9:01

score 586 · Answer 5 · 2026-02-23 08:59:16

586

Views

Show that $\int_0^x f(t)dt$ is compact and injective

Published on 23 Feb 2026 - 8:59

score 657 · Answer 6 · 2026-02-23 09:03:50

657

Views

Showing a sequence of convex functions admits a uniformly convergent subsequence.

Published on 23 Feb 2026 - 9:03

score 190 · Answer 7 · 2026-02-23 09:03:42

190

Views

Consequences of the Arzelà–Ascoli theorem

Published on 23 Feb 2026 - 9:03

score 335 · Answer 8 · 2026-02-23 08:59:24

335

Views

A sequence in a family of continuous functions over a $\sigma$-compact metric space has a uniformly convergent subsequence

Published on 23 Feb 2026 - 8:59

score 194 · Answer 9 · 2026-02-23 08:59:24

194

Views

Prove that a subset G of $C([0,\pi])$ is relatively compact in $C([0,\pi])$

Published on 23 Feb 2026 - 8:59

score 810 · Answer 10 · 2026-02-23 08:54:52

810

Views

Arzela-Ascoli Counter Example?

Published on 23 Feb 2026 - 8:54

score 46 · Answer 11 · 2026-04-09 00:38:34

46

Views

What is definition of ε-tubes?

Published on 09 Apr 2026 - 0:38

score 92 · Answer 12 · 2026-02-23 08:57:50

92

Views

Proving that set of bounded stochastic processes is compact

Published on 23 Feb 2026 - 8:57

score 1k · Answer 13 · 2026-02-23 08:58:17

1k

Views

Applying Arzela-Ascoli to show pointwise convergence on $\mathbb{R}$.

Published on 23 Feb 2026 - 8:58

score 774 · Answer 14 · 2026-02-23 08:53:10

774

Views

Does this function sequence have a convergent subsequence?

Published on 23 Feb 2026 - 8:53

score 1.1k · Answer 15 · 2026-02-23 08:56:35

1.1k

Views

How to understand Arzela-Ascoli theorem?

Published on 23 Feb 2026 - 8:56

List Question

Show that a subset of $C(\mathbb{R})$ is compact with norm $\lVert u\rVert = \sup\lvert\frac{u(x)}{x^2 +1} \rvert$

Ascoli-Arzelà example and equicontinuity

Prove the relative compactness of a sequence in $L^p$

Why is the image under integration of a uniformly bounded subset of $C[a,b]$ necessarily compact?

Show that $\int_0^x f(t)dt$ is compact and injective

Showing a sequence of convex functions admits a uniformly convergent subsequence.

Consequences of the Arzelà–Ascoli theorem

A sequence in a family of continuous functions over a $\sigma$-compact metric space has a uniformly convergent subsequence

Prove that a subset G of $C([0,\pi])$ is relatively compact in $C([0,\pi])$

Arzela-Ascoli Counter Example?

What is definition of ε-tubes?

Proving that set of bounded stochastic processes is compact

Applying Arzela-Ascoli to show pointwise convergence on $\mathbb{R}$.

Does this function sequence have a convergent subsequence?

How to understand Arzela-Ascoli theorem?

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