Question

Let $(X,\mathscr T)$ be a metrizable space such that every metric that generates $\mathscr T$ is bounded. Prove that $X$ is compact.

score 98 · Answer 1 · 2019-04-30 11:32:41

98

Views

Let $(X,\mathscr T)$ be a metrizable space such that every metric that generates $\mathscr T$ is bounded. Prove that $X$ is compact.

Published on 30 Apr 2019 - 11:32

score 306 · Answer 2 · 2019-04-30 14:39:27

306

Views

Railway metric, help showing that the space is bounded but not compact

Published on 30 Apr 2019 - 14:39

score 106 · Answer 3 · 2019-05-02 18:15:34

106

Views

$f:X\rightarrow Y$, with $Y$ compact, is continuous $\Rightarrow$ its graph is closed

Published on 02 May 2019 - 18:15

score 69 · Answer 4 · 2019-05-03 03:32:05

69

Views

Maximal Counterexample to Compactness

Published on 03 May 2019 - 3:32

score 50 · Answer 5 · 2019-05-06 17:01:55

50

Views

Region between two continuous curves is compact

Published on 06 May 2019 - 17:01

score 65 · Answer 6 · 2026-03-27 08:42:52

65

Views

I wondering how can I build a homeomorphism between two squares and a ellipsoid.

Published on 27 Mar 2026 - 8:42

score 257 · Answer 7 · 2026-03-25 07:41:00

257

Views

Closed maps with non-compact fibers

Published on 25 Mar 2026 - 7:41

score 277 · Answer 8 · 2026-03-25 16:06:41

277

Views

Compact space homotopy equivalent to a CW complex

Published on 25 Mar 2026 - 16:06

score 450 · Answer 9 · 2019-05-07 16:34:32

450

Views

Showing $[0,1]$ is compact w.r.t to cofinite topology

Published on 07 May 2019 - 16:34

score 178 · Answer 10 · 2026-03-29 04:48:17

178

Views

Counter-example Aubin-Lions p=1

Published on 29 Mar 2026 - 4:48

score 115 · Answer 11 · 2026-03-25 13:13:32

115

Views

Locally compact limits of countably many finite $T_0$-spaces

Published on 25 Mar 2026 - 13:13

score 2.7k · Answer 12 · 2019-05-08 21:00:29

2.7k

Views

Compactness in normed vector spaces.

Published on 08 May 2019 - 21:00

score 124 · Answer 13 · 2019-05-08 23:49:35

124

Views

Example 1.44 In Rudin's Functional Analysis ("Exhaustion by Compact Sets")

Published on 08 May 2019 - 23:49

score 156 · Answer 14 · 2019-05-09 12:15:42

156

Views

Sequence of points in a nested sequence of sets converges to the point in the limit of the sequence of sets.

Published on 09 May 2019 - 12:15

score 43 · Answer 15 · 2026-03-26 04:53:44

43

Views

A $T_{3 \frac{1}{2}}$ Lindelöf space $X$ is normally placed in $\beta X$

Published on 26 Mar 2026 - 4:53

List Question

Let $(X,\mathscr T)$ be a metrizable space such that every metric that generates $\mathscr T$ is bounded. Prove that $X$ is compact.

Railway metric, help showing that the space is bounded but not compact

$f:X\rightarrow Y$, with $Y$ compact, is continuous $\Rightarrow$ its graph is closed

Maximal Counterexample to Compactness

Region between two continuous curves is compact

I wondering how can I build a homeomorphism between two squares and a ellipsoid.

Closed maps with non-compact fibers

Compact space homotopy equivalent to a CW complex

Showing $[0,1]$ is compact w.r.t to cofinite topology

Counter-example Aubin-Lions p=1

Locally compact limits of countably many finite $T_0$-spaces

Compactness in normed vector spaces.

Example 1.44 In Rudin's Functional Analysis ("Exhaustion by Compact Sets")

Sequence of points in a nested sequence of sets converges to the point in the limit of the sequence of sets.

A $T_{3 \frac{1}{2}}$ Lindelöf space $X$ is normally placed in $\beta X$

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