Question

Can a countable union of disjoint compact Cartesian products be compact?

score 633 · Answer 1 · 2016-08-10 15:19:44

633

Views

Can a countable union of disjoint compact Cartesian products be compact?

Published on 10 Aug 2016 - 15:19

score 50 · Answer 2 · 2026-03-26 06:07:58

50

Views

$X$ non-degenerate Hausdorff space , $f:[0,1] \to X$ is surjective continuous , $a:=\inf \{y\in (0,1]: f([0,y])=X\}$ , then is $a>0$ and $f([0,a])=X$?

Published on 26 Mar 2026 - 6:07

score 64 · Answer 3 · 2016-08-10 21:47:36

64

Views

Well defined solution to a Cauchy problem

Published on 10 Aug 2016 - 21:47

score 672 · Answer 4 · 2026-03-26 21:26:20

672

Views

Show that every locally compact Hausdorff space is embedded in a compact Hausdorff space

Published on 26 Mar 2026 - 21:26

score 166 · Answer 5 · 2016-08-11 10:32:50

166

Views

Is $\mathbb{R}$ with $\tau_{CF}$ and $\tau_{CN}$ locally compact?

Published on 11 Aug 2016 - 10:32

score 208 · Answer 6 · 2026-03-26 14:42:28

208

Views

One point compatification of $(-1,0)\cup (0,1)$

Published on 26 Mar 2026 - 14:42

score 117 · Answer 7 · 2016-08-11 15:15:19

117

Views

When is a space Lindelöf?

Published on 11 Aug 2016 - 15:15

score 142 · Answer 8 · 2026-03-28 13:27:28

142

Views

Complement of $S^1$ in a simply connected oriented surface

Published on 28 Mar 2026 - 13:27

score 545 · Answer 9 · 2016-08-13 06:48:56

545

Views

Compactness of the closed unit ball in the weak* topology: the Banach–Alaoglu theorem

Published on 13 Aug 2016 - 6:48

score 1.1k · Answer 10 · 2016-08-13 17:45:47

1.1k

Views

In the definition of 'Compact set', why do we require the existence of finite subcover for any open cover? Why not countable subcover?

Published on 13 Aug 2016 - 17:45

score 1.9k · Answer 11 · 2026-03-26 12:52:49

1.9k

Views

Show that the Stone–Čech compactification $\beta \mathbb{Z}$ is not metrizable.

Published on 26 Mar 2026 - 12:52

score 911 · Answer 12 · 2016-08-16 16:18:25

911

Views

Are compactly supported Lipschitz functions dense in $L^2$ for some measures?

Published on 16 Aug 2016 - 16:18

score 761 · Answer 13 · 2026-03-31 03:45:43

761

Views

Proving image of compact set via upper semicontinuous set-valued map is compact

Published on 31 Mar 2026 - 3:45

score 33 · Answer 14 · 2016-08-19 01:56:43

33

Views

Is $[0,1]^{[0,1]}$ with the pointwise convergence topology compact?

Published on 19 Aug 2016 - 1:56

score 254 · Answer 15 · 2016-08-19 08:08:41

254

Views

Orthogonal group is compact iff underlying quadradic form is positive or negative definite

Published on 19 Aug 2016 - 8:08

List Question

Can a countable union of disjoint compact Cartesian products be compact?

$X$ non-degenerate Hausdorff space , $f:[0,1] \to X$ is surjective continuous , $a:=\inf \{y\in (0,1]: f([0,y])=X\}$ , then is $a>0$ and $f([0,a])=X$?

Well defined solution to a Cauchy problem

Show that every locally compact Hausdorff space is embedded in a compact Hausdorff space

Is $\mathbb{R}$ with $\tau_{CF}$ and $\tau_{CN}$ locally compact?

One point compatification of $(-1,0)\cup (0,1)$

When is a space Lindelöf?

Complement of $S^1$ in a simply connected oriented surface

Compactness of the closed unit ball in the weak* topology: the Banach–Alaoglu theorem

In the definition of 'Compact set', why do we require the existence of finite subcover for any open cover? Why not countable subcover?

Show that the Stone–Čech compactification $\beta \mathbb{Z}$ is not metrizable.

Are compactly supported Lipschitz functions dense in $L^2$ for some measures?

Proving image of compact set via upper semicontinuous set-valued map is compact

Is $[0,1]^{[0,1]}$ with the pointwise convergence topology compact?

Orthogonal group is compact iff underlying quadradic form is positive or negative definite

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