Question

Using Banach-Alaoglu theorem on $L^1$

score 488 · Answer 1 · 2026-04-13 17:25:33

488

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Using Banach-Alaoglu theorem on $L^1$

Published on 13 Apr 2026 - 17:25

score 1.2k · Answer 2 · 2026-04-14 07:40:19

1.2k

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

Published on 14 Apr 2026 - 7:40

score 258 · Answer 3 · 2026-04-16 07:21:36

258

Views

$A$ closed, $B$ compact. $A$ and $B$ are disjoint. Prove that the distance between them is positive.

Published on 16 Apr 2026 - 7:21

score 255 · Answer 4 · 2026-04-10 19:55:16

255

Views

Does a subcover need to be a proper subcover?

Published on 10 Apr 2026 - 19:55

score 2k · Answer 5 · 2026-04-10 21:52:40

2k

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Let $E$ be the set of all $x \in [0,1]$ whose decimal expansion contains only the digits 4 and 7. Is $E$ compact? - Explanation

Published on 10 Apr 2026 - 21:52

score 271 · Answer 6 · 2026-05-15 21:01:30

271

Views

Convergence of images of a sequence of converging continuous functions

Published on 15 May 2026 - 21:01

score 125 · Answer 7 · 2026-04-15 06:38:39

125

Views

For $(X,d)$ a compact metric space and $ Y \subsetneq X$ there is no isometry $f:X \to Y$.

Published on 15 Apr 2026 - 6:38

score 36 · Answer 8 · 2026-04-13 03:02:51

36

Views

A Non-trivial example of an open cover which will cover $X^{\omega}$ but not any obvious finite sub-cover will cover the same?

Published on 13 Apr 2026 - 3:02

score 128 · Answer 9 · 2026-04-12 23:40:07

128

Views

Bounded metric in compact metric space with continuous function

Published on 12 Apr 2026 - 23:40

score 43 · Answer 10 · 2026-04-11 04:09:07

43

Views

proof compactness of sets

Published on 11 Apr 2026 - 4:09

score 78 · Answer 11 · 2026-04-15 08:38:47

78

Views

Prove that if A & B are disjoint open sets then their intersection is compact.

Published on 15 Apr 2026 - 8:38

score 114 · Answer 12 · 2026-04-14 08:38:29

114

Views

A difficulty in understanding the finite intersection property.

Published on 14 Apr 2026 - 8:38

score 287 · Answer 13 · 2026-05-11 05:19:22

287

Views

Example of a locally compact + Hausdorff + ¬normal + connected space

Published on 11 May 2026 - 5:19

score 115 · Answer 14 · 2026-04-14 11:11:09

115

Views

Is this proof of the Bolzano-Weierstrass theorem correct?

Published on 14 Apr 2026 - 11:11

score 343 · Answer 15 · 2026-04-12 17:58:23

343

Views

Question on step in proof of Weierstrass thereom (of max and min)

Published on 12 Apr 2026 - 17:58

List Question

Using Banach-Alaoglu theorem on $L^1$

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

$A$ closed, $B$ compact. $A$ and $B$ are disjoint. Prove that the distance between them is positive.

Does a subcover need to be a proper subcover?

Let $E$ be the set of all $x \in [0,1]$ whose decimal expansion contains only the digits 4 and 7. Is $E$ compact? - Explanation

Convergence of images of a sequence of converging continuous functions

For $(X,d)$ a compact metric space and $ Y \subsetneq X$ there is no isometry $f:X \to Y$.

A Non-trivial example of an open cover which will cover $X^{\omega}$ but not any obvious finite sub-cover will cover the same?

Bounded metric in compact metric space with continuous function

proof compactness of sets

Prove that if A & B are disjoint open sets then their intersection is compact.

A difficulty in understanding the finite intersection property.

Example of a locally compact + Hausdorff + ¬normal + connected space

Is this proof of the Bolzano-Weierstrass theorem correct?

Question on step in proof of Weierstrass thereom (of max and min)

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