Question

Using Banach-Alaoglu theorem on $L^1$

score 486 · Answer 1 · 2026-03-28 16:12:53

486

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Using Banach-Alaoglu theorem on $L^1$

Published on 28 Mar 2026 - 16:12

score 1.2k · Answer 2 · 2026-03-25 15:12:14

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 25 Mar 2026 - 15:12

score 255 · Answer 3 · 2019-03-08 17:45:03

255

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

Published on 08 Mar 2019 - 17:45

score 252 · Answer 4 · 2019-03-09 13:20:06

252

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Does a subcover need to be a proper subcover?

Published on 09 Mar 2019 - 13:20

score 2k · Answer 5 · 2019-03-10 02:27:57

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 Mar 2019 - 2:27

score 268 · Answer 6 · 2026-03-30 01:30:06

268

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Convergence of images of a sequence of converging continuous functions

Published on 30 Mar 2026 - 1:30

score 122 · Answer 7 · 2019-03-10 22:50:49

122

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

Published on 10 Mar 2019 - 22:50

score 33 · Answer 8 · 2019-03-11 05:03:34

33

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 11 Mar 2019 - 5:03

score 125 · Answer 9 · 2019-03-11 13:10:18

125

Views

Bounded metric in compact metric space with continuous function

Published on 11 Mar 2019 - 13:10

score 40 · Answer 10 · 2019-03-11 21:14:47

40

Views

proof compactness of sets

Published on 11 Mar 2019 - 21:14

score 75 · Answer 11 · 2019-03-12 04:25:58

75

Views

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

Published on 12 Mar 2019 - 4:25

score 111 · Answer 12 · 2019-03-12 05:10:21

111

Views

A difficulty in understanding the finite intersection property.

Published on 12 Mar 2019 - 5:10

score 285 · Answer 13 · 2026-03-25 08:07:36

285

Views

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

Published on 25 Mar 2026 - 8:07

score 112 · Answer 14 · 2019-03-12 13:58:07

112

Views

Is this proof of the Bolzano-Weierstrass theorem correct?

Published on 12 Mar 2019 - 13:58

score 341 · Answer 15 · 2026-03-28 23:59:35

341

Views

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

Published on 28 Mar 2026 - 23:59

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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