Question

$(X,d)$ is a metric space such that every continuous function $f: X \rightarrow \mathbb{R}$ is bounded. Prove $X$ is complete.

score 210 · Answer 1 · 2019-08-26 22:09:34

210

Views

$(X,d)$ is a metric space such that every continuous function $f: X \rightarrow \mathbb{R}$ is bounded. Prove $X$ is complete.

Published on 26 Aug 2019 - 22:09

score 152 · Answer 2 · 2019-08-27 00:55:21

152

Views

If $x_n \rightarrow x$ and $Ax_n \rightharpoonup y$, why does $y = Ax$?

Published on 27 Aug 2019 - 0:55

score 47 · Answer 3 · 2019-08-27 13:41:51

47

Views

Let $\sum a_{k}$ be a convergent series in a Banach space $E$. Show that $\lim_{n \to \infty} r_n =0$

Published on 27 Aug 2019 - 13:41

score 351 · Answer 4 · 2026-02-23 04:46:00

351

Views

Spectral theory; separation of spectrum, eigenprojections

Published on 23 Feb 2026 - 4:46

score 121 · Answer 5 · 2026-03-28 08:49:02

121

Views

Local lifting property for Banach Spaces

Published on 28 Mar 2026 - 8:49

score 51 · Answer 6 · 2026-03-26 06:29:53

51

Views

Problem on family of Banach spaces

Published on 26 Mar 2026 - 6:29

score 130 · Answer 7 · 2019-09-02 13:00:37

130

Views

Looking for subspaces that are isomorphic to $\ell_1$.

Published on 02 Sep 2019 - 13:00

score 195 · Answer 8 · 2019-09-03 14:13:36

195

Views

Prove that $\langle \ell^p, \|\cdot\|_p \rangle$ is a Banach space

Published on 03 Sep 2019 - 14:13

score 590 · Answer 9 · 2019-09-04 12:40:16

590

Views

Is it true that every Banach space has Bolzano Weierstrass property?

Published on 04 Sep 2019 - 12:40

score 107 · Answer 10 · 2019-09-04 17:59:07

107

Views

Construction of bounded sequence in $l_{2}$ which does not have convergent subsequence

Published on 04 Sep 2019 - 17:59

score 61 · Answer 11 · 2019-09-04 23:16:54

61

Views

Sequence not in Schreier space

Published on 04 Sep 2019 - 23:16

score 129 · Answer 12 · 2019-09-05 00:21:13

129

Views

To understand the distance function in (X, || . || ) × ( X, ||. || )

Published on 05 Sep 2019 - 0:21

score 108 · Answer 13 · 2019-09-05 05:05:45

108

Views

What is the space of $\mathbb{R}^n$ in relation to a Banach space?

Published on 05 Sep 2019 - 5:05

score 32 · Answer 14 · 2019-09-05 05:57:55

32

Views

On random vectors and scalar products

Published on 05 Sep 2019 - 5:57

score 75 · Answer 15 · 2026-03-26 06:29:49

75

Views

Complete subset of $X$ such that elements are of a fixed norm value implies $X$ Banach

Published on 26 Mar 2026 - 6:29

List Question

$(X,d)$ is a metric space such that every continuous function $f: X \rightarrow \mathbb{R}$ is bounded. Prove $X$ is complete.

If $x_n \rightarrow x$ and $Ax_n \rightharpoonup y$, why does $y = Ax$?

Let $\sum a_{k}$ be a convergent series in a Banach space $E$. Show that $\lim_{n \to \infty} r_n =0$

Spectral theory; separation of spectrum, eigenprojections

Local lifting property for Banach Spaces

Problem on family of Banach spaces

Looking for subspaces that are isomorphic to $\ell_1$.

Prove that $\langle \ell^p, \|\cdot\|_p \rangle$ is a Banach space

Is it true that every Banach space has Bolzano Weierstrass property?

Construction of bounded sequence in $l_{2}$ which does not have convergent subsequence

Sequence not in Schreier space

To understand the distance function in (X, || . || ) × ( X, ||. || )

What is the space of $\mathbb{R}^n$ in relation to a Banach space?

On random vectors and scalar products

Complete subset of $X$ such that elements are of a fixed norm value implies $X$ Banach

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