Question

Continuity and compactness of this operator?

score 58 · Answer 1 · 2026-05-15 06:48:54

58

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Continuity and compactness of this operator?

Published on 15 May 2026 - 6:48

score 54 · Answer 2 · 2026-04-10 23:54:30

54

Views

How to show that $\infty$ is isolated?

Published on 10 Apr 2026 - 23:54

score 667 · Answer 3 · 2026-05-11 02:54:34

667

Views

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

Published on 11 May 2026 - 2:54

score 355 · Answer 4 · 2026-04-12 11:40:28

355

Views

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

Published on 12 Apr 2026 - 11:40

score 159 · Answer 5 · 2026-04-16 00:45:14

159

Views

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

Published on 16 Apr 2026 - 0:45

score 257 · Answer 6 · 2026-05-13 23:32:53

257

Views

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

Published on 13 May 2026 - 23:32

score 285 · Answer 7 · 2026-05-10 21:56:04

285

Views

Proof verification for some properties of convex hulls

Published on 10 May 2026 - 21:56

score 1.1k · Answer 8 · 2026-04-14 06:37:07

1.1k

Views

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

Published on 14 Apr 2026 - 6:37

score 69 · Answer 9 · 2026-04-11 10:29:24

69

Views

Product of compact set and a vector

Published on 11 Apr 2026 - 10:29

score 121 · Answer 10 · 2026-04-13 03:41:09

121

Views

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

Published on 13 Apr 2026 - 3:41

score 57 · Answer 11 · 2026-05-13 22:10:04

57

Views

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

Published on 13 May 2026 - 22:10

score 26 · Answer 12 · 2026-04-14 05:38:05

26

Views

Compactness of a set given by two equalities

Published on 14 Apr 2026 - 5:38

score 301 · Answer 13 · 2026-04-13 22:10:05

301

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 13 Apr 2026 - 22:10

score 1.8k · Answer 14 · 2026-04-13 20:54:09

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 13 Apr 2026 - 20:54

score 30 · Answer 15 · 2026-04-17 13:02:44

30

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 17 Apr 2026 - 13:02

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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