Question

Can a point and a compact set in a Tychonoff space be separated by a continuous function into an arbitrary finite dimension Lie group?

score 42 · Answer 1 · 2015-12-20 10:48:00

42

Views

Can a point and a compact set in a Tychonoff space be separated by a continuous function into an arbitrary finite dimension Lie group?

Published on 20 Dec 2015 - 10:48

score 928 · Answer 2 · 2016-01-03 09:04:31

928

Views

Example of a Hausdorff space that is not completely Hausdorff

Published on 03 Jan 2016 - 9:04

score 258 · Answer 3 · 2016-01-06 15:44:35

258

Views

$(X,\tau)$ be a finite topological space , then is it Regular if ( and only if ) it has a basis which forms a partition of $X$?

Published on 06 Jan 2016 - 15:44

score 117 · Answer 4 · 2016-01-09 15:15:38

117

Views

Separation axioms and when does there exist a connected space all whose proper connected subspaces are homeomorphic to the whole space?

Published on 09 Jan 2016 - 15:15

score 269 · Answer 5 · 2016-01-10 09:50:44

269

Views

A direct proof that this space is normal

Published on 10 Jan 2016 - 9:50

score 792 · Answer 6 · 2016-01-10 22:49:18

792

Views

T3 space which does not satisfy certain condition

Published on 10 Jan 2016 - 22:49

score 238 · Answer 7 · 2026-03-07 11:04:23

238

Views

Is every Hausdorff homogeneous space also regular?

Published on 07 Mar 2026 - 11:04

score 2.1k · Answer 8 · 2016-01-24 00:11:51

2.1k

Views

$X$ normal $f:X \longrightarrow Y$ continuous, surjective, closed $\Longrightarrow$ $Y$ normal

Published on 24 Jan 2016 - 0:11

score 337 · Answer 9 · 2016-02-01 05:28:47

337

Views

Subset of first countable space closed iff intersection with every compact set is closed.

Published on 01 Feb 2016 - 5:28

score 1.1k · Answer 10 · 2016-02-02 03:17:13

1.1k

Views

Show that every open set in second countable LCH space is $\sigma$-compact

Published on 02 Feb 2016 - 3:17

score 1.6k · Answer 11 · 2016-02-09 03:25:25

1.6k

Views

Prove that the space $\Bbb R_K$ is not regular.

Published on 09 Feb 2016 - 3:25

score 4.8k · Answer 12 · 2016-02-10 04:36:55

4.8k

Views

Show that a connected regular space having more than one point is uncountable

Published on 10 Feb 2016 - 4:36

score 235 · Answer 13 · 2016-02-14 09:29:50

235

Views

Show that $X$ is Hausdorff.

Published on 14 Feb 2016 - 9:29

score 975 · Answer 14 · 2016-02-16 15:29:35

975

Views

Is there a countably compact sequential non-$T_2$ space that is not sequentially compact?

Published on 16 Feb 2016 - 15:29

score 598 · Answer 15 · 2026-03-26 02:59:17

598

Views

Separation of a set

Published on 26 Mar 2026 - 2:59

List Question

Can a point and a compact set in a Tychonoff space be separated by a continuous function into an arbitrary finite dimension Lie group?

Example of a Hausdorff space that is not completely Hausdorff

$(X,\tau)$ be a finite topological space , then is it Regular if ( and only if ) it has a basis which forms a partition of $X$?

Separation axioms and when does there exist a connected space all whose proper connected subspaces are homeomorphic to the whole space?

A direct proof that this space is normal

T3 space which does not satisfy certain condition

Is every Hausdorff homogeneous space also regular?

$X$ normal $f:X \longrightarrow Y$ continuous, surjective, closed $\Longrightarrow$ $Y$ normal

Subset of first countable space closed iff intersection with every compact set is closed.

Show that every open set in second countable LCH space is $\sigma$-compact

Prove that the space $\Bbb R_K$ is not regular.

Show that a connected regular space having more than one point is uncountable

Show that $X$ is Hausdorff.

Is there a countably compact sequential non-$T_2$ space that is not sequentially compact?

Separation of a set

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