Question

Under which $T$ axiom can you separate disjoint closed and compact set? Compact and compact set?

score 785 · Answer 1 · 2026-03-26 06:07:06

785

Views

Under which $T$ axiom can you separate disjoint closed and compact set? Compact and compact set?

Published on 26 Mar 2026 - 6:07

score 3.3k · Answer 2 · 2016-08-01 03:14:35

3.3k

Views

Is $\mathbb{R}$ compact under the co-countable and co-finite topologies?

Published on 01 Aug 2016 - 3:14

score 472 · Answer 3 · 2016-08-01 05:32:39

472

Views

Is $\mathbb{R}$ with the particular point topology and open half line topology compact?

Published on 01 Aug 2016 - 5:32

score 52 · Answer 4 · 2016-08-02 22:35:40

52

Views

Where $\mathbf S$ is the collection of all real sequences, is $K$ compact w.r.t. the metric $d_\mathbf{S}$?

Published on 02 Aug 2016 - 22:35

score 155 · Answer 5 · 2026-03-29 07:34:43

155

Views

Is this subset of $\ell_1$ compact?

Published on 29 Mar 2026 - 7:34

score 756 · Answer 6 · 2016-08-04 05:57:17

756

Views

Compact subset of $C[0,1]$

Published on 04 Aug 2016 - 5:57

score 98 · Answer 7 · 2026-03-25 14:25:30

98

Views

$T$ be a contraction on an infinite complete metric space , then is there a non singleton compact subset of $X$ which is invariant under $T$?

Published on 25 Mar 2026 - 14:25

score 212 · Answer 8 · 2026-03-26 12:53:10

212

Views

Does the function $f(x)=x^2$ admit a continuous extension to the Stone-Cech compactification?

Published on 26 Mar 2026 - 12:53

score 154 · Answer 9 · 2016-08-08 19:02:48

154

Views

Continuous function with compact set

Published on 08 Aug 2016 - 19:02

score 708 · Answer 10 · 2026-03-26 12:58:05

708

Views

What does the 1-point compactification of disjoint open intervals look like?

Published on 26 Mar 2026 - 12:58

score 4.2k · Answer 11 · 2026-03-26 11:17:34

4.2k

Views

Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff

Published on 26 Mar 2026 - 11:17

score 2.5k · Answer 12 · 2026-04-02 13:23:57

2.5k

Views

Show that $\mathbb{Q}$ is not locally compact with a characterization of local compactness

Published on 02 Apr 2026 - 13:23

score 3.8k · Answer 13 · 2016-08-09 21:27:41

3.8k

Views

Closed and open subsets of locally compact Hausdorff space are locally compact

Published on 09 Aug 2016 - 21:27

score 303 · Answer 14 · 2016-08-10 12:48:43

303

Views

Is this the right way to prove finite cartesian product of compact sets is compact

Published on 10 Aug 2016 - 12:48

score 93 · Answer 15 · 2016-08-10 15:17:24

93

Views

Chicken and egg problem: show that every singleton in a hereditarily compact Hausdorff space is clopen

Published on 10 Aug 2016 - 15:17

List Question

Under which $T$ axiom can you separate disjoint closed and compact set? Compact and compact set?

Is $\mathbb{R}$ compact under the co-countable and co-finite topologies?

Is $\mathbb{R}$ with the particular point topology and open half line topology compact?

Where $\mathbf S$ is the collection of all real sequences, is $K$ compact w.r.t. the metric $d_\mathbf{S}$?

Is this subset of $\ell_1$ compact?

Compact subset of $C[0,1]$

$T$ be a contraction on an infinite complete metric space , then is there a non singleton compact subset of $X$ which is invariant under $T$?

Does the function $f(x)=x^2$ admit a continuous extension to the Stone-Cech compactification?

Continuous function with compact set

What does the 1-point compactification of disjoint open intervals look like?

Show that the one point compactification of $\mathbb{Q}$ is not Hausdorff

Show that $\mathbb{Q}$ is not locally compact with a characterization of local compactness

Closed and open subsets of locally compact Hausdorff space are locally compact

Is this the right way to prove finite cartesian product of compact sets is compact

Chicken and egg problem: show that every singleton in a hereditarily compact Hausdorff space is clopen

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