Question

Show this set is closed

score 67 · Answer 1 · 2014-10-28 00:29:00

67

Views

Show this set is closed

Published on 28 Oct 2014 - 0:29

score 54 · Answer 2 · 2026-03-25 23:10:13

54

Views

A set of differential forms, uniformly bounded with their Laplacians, is precompact in $L^2$.

Published on 25 Mar 2026 - 23:10

score 167 · Answer 3 · 2026-03-26 22:55:42

167

Views

Correctness of reasoning about finiteness of degree of a covering map

Published on 26 Mar 2026 - 22:55

score 2.4k · Answer 4 · 2014-10-31 16:32:48

2.4k

Views

Show that the unit sphere with centre $0$ in $\mathbb{R}^d$ is compact.

Published on 31 Oct 2014 - 16:32

score 170 · Answer 5 · 2014-11-01 10:16:06

170

Views

Kelley's topology : A topological space X is compact iff each nest of closed non-void sets has a non-void intersection.

Published on 01 Nov 2014 - 10:16

score 100 · Answer 6 · 2014-11-01 18:04:02

100

Views

Would the following proof be wrong? (About the intersections of compact subsets)

Published on 01 Nov 2014 - 18:04

score 5.1k · Answer 7 · 2026-04-02 21:47:27

5.1k

Views

Compact set in R that is not convex?

Published on 02 Apr 2026 - 21:47

score 89 · Answer 8 · 2014-11-02 12:54:23

89

Views

Compactness of the sum of line segments

Published on 02 Nov 2014 - 12:54

score 387 · Answer 9 · 2026-03-30 03:35:32

387

Views

compactness criterion for random variables in L2

Published on 30 Mar 2026 - 3:35

score 933 · Answer 10 · 2014-11-02 20:39:16

933

Views

Motivation for the Definition of Compact Sets

Published on 02 Nov 2014 - 20:39

score 115 · Answer 11 · 2014-11-03 05:13:15

115

Views

Show $K$ is Compact.

Published on 03 Nov 2014 - 5:13

score 835 · Answer 12 · 2026-03-25 10:57:26

835

Views

Show that the set of uniformly Lipschitz functions vanishing at $0$ is compact in $C[0,1]$

Published on 25 Mar 2026 - 10:57

score 760 · Answer 13 · 2014-11-04 07:19:03

760

Views

Let A and B be disjoint closed subsets of Rn. Define d(A,B)=inf{∥a−b∥:a∈A and b∈B}. Show that if A={a} is a singleton, then d(A,B)>0.

Published on 04 Nov 2014 - 7:19

score 6.8k · Answer 14 · 2014-11-04 15:52:26

6.8k

Views

Hilbert cube is compact

Published on 04 Nov 2014 - 15:52

score 3.7k · Answer 15 · 2014-11-04 18:00:23

3.7k

Views

If every continuous function $f: A \rightarrow \mathbb{R}$ is bounded, then A is compact.

Published on 04 Nov 2014 - 18:00

List Question

Show this set is closed

A set of differential forms, uniformly bounded with their Laplacians, is precompact in $L^2$.

Correctness of reasoning about finiteness of degree of a covering map

Show that the unit sphere with centre $0$ in $\mathbb{R}^d$ is compact.

Kelley's topology : A topological space X is compact iff each nest of closed non-void sets has a non-void intersection.

Would the following proof be wrong? (About the intersections of compact subsets)

Compact set in R that is not convex?

Compactness of the sum of line segments

compactness criterion for random variables in L2

Motivation for the Definition of Compact Sets

Show $K$ is Compact.

Show that the set of uniformly Lipschitz functions vanishing at $0$ is compact in $C[0,1]$

Let A and B be disjoint closed subsets of Rn. Define d(A,B)=inf{∥a−b∥:a∈A and b∈B}. Show that if A={a} is a singleton, then d(A,B)>0.

Hilbert cube is compact

If every continuous function $f: A \rightarrow \mathbb{R}$ is bounded, then A is compact.

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