Question

Infinite intersection of compact sets empty implies a finite intersection is also empty

score 805 · Answer 1 · 2026-04-15 02:29:24

805

Views

Infinite intersection of compact sets empty implies a finite intersection is also empty

Published on 15 Apr 2026 - 2:29

score 422 · Answer 2 · 2026-04-10 21:47:38

422

Views

Is there an open subspace of a locally compact space that is not locally compact?

Published on 10 Apr 2026 - 21:47

score 11.3k · Answer 3 · 2026-04-05 09:19:15

11.3k

Views

Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?

Published on 05 Apr 2026 - 9:19

score 523 · Answer 4 · 2026-04-14 18:22:47

523

Views

Proving T is a contraction

Published on 14 Apr 2026 - 18:22

score 1.6k · Answer 5 · 2026-04-14 21:43:47

1.6k

Views

Intersection of clopen sets that contain x is the connected component of x (if X is compact)

Published on 14 Apr 2026 - 21:43

score 1.2k · Answer 6 · 2026-04-15 03:19:46

1.2k

Views

For a Compact Metric Space $T: X\to X$ has unique fixed point

Published on 15 Apr 2026 - 3:19

score 687 · Answer 7 · 2026-04-13 04:47:45

687

Views

Number of connected components of the complement of a compact

Published on 13 Apr 2026 - 4:47

score 71 · Answer 8 · 2026-04-13 23:18:13

71

Views

Is a metrizable space $X$ compact $\iff \exists x,y$ such that $d(x,y) = \sup d(u,v)_{u,v \in X}$?

Published on 13 Apr 2026 - 23:18

score 90 · Answer 9 · 2026-04-11 16:20:23

90

Views

Can I show that intersection of finitely many compact subsets is non-zero

Published on 11 Apr 2026 - 16:20

score 102 · Answer 10 · 2026-04-14 12:24:44

102

Views

Compact Subset of a Domain in $\mathbb{C}$

Published on 14 Apr 2026 - 12:24

score 266 · Answer 11 · 2026-04-13 06:47:18

266

Views

Show compactness

Published on 13 Apr 2026 - 6:47

score 704 · Answer 12 · 2026-04-13 04:48:09

704

Views

A bounded net with a unique limit point must be convergent

Published on 13 Apr 2026 - 4:48

score 77 · Answer 13 · 2026-04-10 04:09:05

77

Views

Checking for varification: Proof - continuous function on a compact metric spaces is uniformly continuous

Published on 10 Apr 2026 - 4:09

score 91 · Answer 14 · 2026-04-14 07:46:01

91

Views

Increasing sequence of compacts of $(0,1)$

Published on 14 Apr 2026 - 7:46

score 158 · Answer 15 · 2026-04-14 14:36:20

158

Views

Prove that $d(x,F)>0$, where F is a family of closed subsets with an empty intersection

Published on 14 Apr 2026 - 14:36

List Question

Infinite intersection of compact sets empty implies a finite intersection is also empty

Is there an open subspace of a locally compact space that is not locally compact?

Why is $[0, 1] \cap \mathbb{Q}$ not compact in $\mathbb{Q}$?

Proving T is a contraction

Intersection of clopen sets that contain x is the connected component of x (if X is compact)

For a Compact Metric Space $T: X\to X$ has unique fixed point

Number of connected components of the complement of a compact

Is a metrizable space $X$ compact $\iff \exists x,y$ such that $d(x,y) = \sup d(u,v)_{u,v \in X}$?

Can I show that intersection of finitely many compact subsets is non-zero

Compact Subset of a Domain in $\mathbb{C}$

Show compactness

A bounded net with a unique limit point must be convergent

Checking for varification: Proof - continuous function on a compact metric spaces is uniformly continuous

Increasing sequence of compacts of $(0,1)$

Prove that $d(x,F)>0$, where F is a family of closed subsets with an empty intersection

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