Question

Continuity and compactness of this operator?

score 54 · Answer 1 · 2026-03-26 01:01:49

54

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Continuity and compactness of this operator?

Published on 26 Mar 2026 - 1:01

score 52 · Answer 2 · 2026-03-29 17:43:17

52

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How to show that $\infty$ is isolated?

Published on 29 Mar 2026 - 17:43

score 664 · Answer 3 · 2026-03-25 06:21:01

664

Views

Proof Verification: Show that if Y is compact, then the projection is a closed map

Published on 25 Mar 2026 - 6:21

score 353 · Answer 4 · 2026-03-25 19:05:52

353

Views

Using the quotient manifold theorem to show real projective spaces are smooth manifolds

Published on 25 Mar 2026 - 19:05

score 156 · Answer 5 · 2019-03-02 20:03:10

156

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Prove the set $K = \{0\} \cup \{\frac{1}{n} \in \mathbb{R} : n \in \mathbb{N} \}$ is compact without Heine-Borel

Published on 02 Mar 2019 - 20:03

score 254 · Answer 6 · 2026-03-25 17:40:22

254

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If $X$ is reflexive and $A \in \mathcal{L}(c_0,X)$ then show that $A$ is a compact operator.

Published on 25 Mar 2026 - 17:40

score 281 · Answer 7 · 2026-03-25 04:57:29

281

Views

Proof verification for some properties of convex hulls

Published on 25 Mar 2026 - 4:57

score 1.1k · Answer 8 · 2019-03-03 16:32:00

1.1k

Views

Is this proof that a continuous image of a compact metric space is compact correct?

Published on 03 Mar 2019 - 16:32

score 66 · Answer 9 · 2019-03-04 22:42:37

66

Views

Product of compact set and a vector

Published on 04 Mar 2019 - 22:42

score 119 · Answer 10 · 2026-03-28 15:21:30

119

Views

Counterexample of any infinite union of open balls is a complement of a compact set in $R^d$.

Published on 28 Mar 2026 - 15:21

score 52 · Answer 11 · 2026-03-25 19:06:21

52

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$A(D) \subseteq Y$ is compact if $A \in \mathcal{L}_c(X,Y)$, $X$ reflexive, $Y$ Banach and $D$ closed, convex and bounded.

Published on 25 Mar 2026 - 19:06

score 23 · Answer 12 · 2019-03-05 19:56:18

23

Views

Compactness of a set given by two equalities

Published on 05 Mar 2019 - 19:56

score 299 · Answer 13 · 2026-03-26 01:08:00

299

Views

Prob. 5, Sec. 28, in Munkres' TOPOLOGY, 2nd ed: $X$ is countably compact iff any nested sequence of nonempty closed sets has nonempty intersection

Published on 26 Mar 2026 - 1:08

score 1.8k · Answer 14 · 2026-03-26 01:04:38

1.8k

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Prob. 7 (a), Sec. 28, in Munkres' TOPOLOGY, 2nd ed: A contraction of a compact metric space has a unique fixed point

Published on 26 Mar 2026 - 1:04

score 28 · Answer 15 · 2019-03-06 21:47:49

28

Views

$\lim\limits_{u\rightarrow\infty}|F_1(u,x)-F_2(u,x)|=0,\forall x\geq0\implies\lim\limits_{u\rightarrow\infty}\sup_{x\geq0}|F_1(u,x)-F_2(u,x)|=0$?

Published on 06 Mar 2019 - 21:47

List Question

Continuity and compactness of this operator?

How to show that $\infty$ is isolated?

Proof Verification: Show that if Y is compact, then the projection is a closed map

Using the quotient manifold theorem to show real projective spaces are smooth manifolds

Prove the set $K = \{0\} \cup \{\frac{1}{n} \in \mathbb{R} : n \in \mathbb{N} \}$ is compact without Heine-Borel

If $X$ is reflexive and $A \in \mathcal{L}(c_0,X)$ then show that $A$ is a compact operator.

Proof verification for some properties of convex hulls

Is this proof that a continuous image of a compact metric space is compact correct?

Product of compact set and a vector

Counterexample of any infinite union of open balls is a complement of a compact set in $R^d$.

$A(D) \subseteq Y$ is compact if $A \in \mathcal{L}_c(X,Y)$, $X$ reflexive, $Y$ Banach and $D$ closed, convex and bounded.

Compactness of a set given by two equalities

Prob. 5, Sec. 28, in Munkres' TOPOLOGY, 2nd ed: $X$ is countably compact iff any nested sequence of nonempty closed sets has nonempty intersection

Prob. 7 (a), Sec. 28, in Munkres' TOPOLOGY, 2nd ed: A contraction of a compact metric space has a unique fixed point

$\lim\limits_{u\rightarrow\infty}|F_1(u,x)-F_2(u,x)|=0,\forall x\geq0\implies\lim\limits_{u\rightarrow\infty}\sup_{x\geq0}|F_1(u,x)-F_2(u,x)|=0$?

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