Question

If $X$ is complete, then every subset of $X$ that is closed and totally bounded is also compact. Does the converse hold?

score 178 · Answer 1 · 2014-03-28 15:14:28

If $X$ is complete, then every subset of $X$ that is closed and totally bounded is also compact. Does the converse hold?

score 312 · Answer 2 · 2026-04-12 10:46:45

312

Views

Borel-set, open, measurable function.

Published on 12 Apr 2026 - 10:46

score 1.1k · Answer 3 · 2026-04-04 00:37:42

1.1k

Views

What is the exact definition of a bounded subset in a metric space?

Published on 04 Apr 2026 - 0:37

score 138 · Answer 4 · 2026-04-12 02:37:59

138

Views

How to show the completeness of the space of Fourier transforms $\mathcal{F}L^{1}$?

Published on 12 Apr 2026 - 2:37

score 96 · Answer 5 · 2026-03-26 16:10:17

96

Views

Endowing a metric on the torus from the euclidian metric of its covering space, the plane

Published on 26 Mar 2026 - 16:10

score 318 · Answer 6 · 2026-04-12 14:49:33

318

Views

Convergence of circles in Hausdorff distance

Published on 12 Apr 2026 - 14:49

score 3.4k · Answer 7 · 2026-04-12 12:59:52

3.4k

Views

Hausdorff distance and intersection

Published on 12 Apr 2026 - 12:59

score 100 · Answer 8 · 2026-04-12 14:19:42

100

Views

proving a metric

Published on 12 Apr 2026 - 14:19

score 1.1k · Answer 9 · 2026-04-11 17:55:30

1.1k

Views

Isometry groups acting transitively

Published on 11 Apr 2026 - 17:55

score 3.9k · Answer 10 · 2014-03-30 22:59:49

3.9k

Views

A metric space is compact if and only if its complete and totally bounded.

Published on 30 Mar 2014 - 22:59

score 841 · Answer 11 · 2014-03-31 07:47:00

841

Views

proving topological equivalence

Published on 31 Mar 2014 - 7:47

score 33 · Answer 12 · 2014-03-31 11:48:30

33

Views

Verify why this is not a metric $d(x,y)=\|x-y\|_p$ ( $\|x\|_p=p^{-h}$ if $x=p^h\dfrac{m}{n}$).

Published on 31 Mar 2014 - 11:48

score 784 · Answer 13 · 2014-03-31 14:00:31

784

Views

The "intersection property" of the symmetric difference metric

Published on 31 Mar 2014 - 14:00

score 5.9k · Answer 14 · 2026-03-30 06:12:43

5.9k

Views

Example of two open balls such that the one with the smaller radius contains the one with the larger radius.

Published on 30 Mar 2026 - 6:12

score 62 · Answer 15 · 2014-03-31 20:12:04

62

Views

Proving a basis exists

Published on 31 Mar 2014 - 20:12

List Question

If $X$ is complete, then every subset of $X$ that is closed and totally bounded is also compact. Does the converse hold?

Borel-set, open, measurable function.

What is the exact definition of a bounded subset in a metric space?

How to show the completeness of the space of Fourier transforms $\mathcal{F}L^{1}$?

Endowing a metric on the torus from the euclidian metric of its covering space, the plane

Convergence of circles in Hausdorff distance

Hausdorff distance and intersection

proving a metric

Isometry groups acting transitively

A metric space is compact if and only if its complete and totally bounded.

proving topological equivalence

Verify why this is not a metric $d(x,y)=\|x-y\|_p$ ( $\|x\|_p=p^{-h}$ if $x=p^h\dfrac{m}{n}$).

The "intersection property" of the symmetric difference metric

Example of two open balls such that the one with the smaller radius contains the one with the larger radius.

Proving a basis exists

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