Question

numerably paracompact spaces

score 43 · Answer 1 · 2020-10-07 23:54:37

43

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numerably paracompact spaces

Published on 07 Oct 2020 - 23:54

score 100 · Answer 2 · 2020-10-25 15:13:59

100

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Let $ (X, \tau) $ be a paracompact space $ T_2 $ and $ A \subset X $. If $A$ is closed, then the quotient space $X / A$ is paracompact and $T_2$.

Published on 25 Oct 2020 - 15:13

score 40 · Answer 3 · 2020-10-28 20:06:30

Let $ X $ be a topological space, paracompact, $T_2$. Let $S \subset X$, with $S$ is generalized-$F_{\sigma}$ then $ S $ is paracompact.

score 86 · Answer 4 · 2020-11-03 22:46:16

86

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Is a closure-preserving union of closed paracompact subspaces paracompact?

Published on 03 Nov 2020 - 22:46

score 244 · Answer 5 · 2020-11-07 01:36:36

244

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Munkres section 41, expansion lemma and paracompact spaces

Published on 07 Nov 2020 - 1:36

score 347 · Answer 6 · 2020-11-08 21:28:08

If for an open cover there exists a partition of unity subordinated to it, then the cover has an open locally finite refinement.

score 258 · Answer 7 · 2020-11-09 12:40:24

258

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countable union of closed paracompact subspaces

Published on 09 Nov 2020 - 12:40

score 89 · Answer 8 · 2020-11-13 07:45:23

89

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Perfect image of a metrizable space is metrizable.

Published on 13 Nov 2020 - 7:45

score 140 · Answer 9 · 2026-02-23 02:56:49

140

Views

$\mathbb R^{\omega}$ in the box topology not paracompact?

Published on 23 Feb 2026 - 2:56

score 28 · Answer 10 · 2021-04-04 13:10:26

28

Views

Does normal space guarantees existence of normal cover

Published on 04 Apr 2021 - 13:10

score 286 · Answer 11 · 2021-05-09 08:14:17

286

Views

Why do we define partitions of unity to be locally finite instead of pointwise finite?

Published on 09 May 2021 - 8:14

score 100 · Answer 12 · 2021-05-20 21:35:12

100

Views

Help with proof of Lemma 1 in "A note on paracompact spaces" (Michael, PAMS 4 (5), 1953)

Published on 20 May 2021 - 21:35

score 26 · Answer 13 · 2021-06-07 18:33:24

26

Views

locally finite family $ \mathcal{A} $

Published on 07 Jun 2021 - 18:33

score 156 · Answer 14 · 2021-07-01 06:03:26

156

Views

show that every countable subcover is $\sigma$- locally finite refinement. (every regular Lindelöf space is paracompact)

Published on 01 Jul 2021 - 6:03

score 210 · Answer 15 · 2021-07-03 07:45:28

210

Views

Paracompactness of topological group.

Published on 03 Jul 2021 - 7:45

List Question

numerably paracompact spaces

Let $ (X, \tau) $ be a paracompact space $ T_2 $ and $ A \subset X $. If $A$ is closed, then the quotient space $X / A$ is paracompact and $T_2$.

Let $ X $ be a topological space, paracompact, $T_2$. Let $S \subset X$, with $S$ is generalized-$F_{\sigma}$ then $ S $ is paracompact.

Is a closure-preserving union of closed paracompact subspaces paracompact?

Munkres section 41, expansion lemma and paracompact spaces

If for an open cover there exists a partition of unity subordinated to it, then the cover has an open locally finite refinement.

countable union of closed paracompact subspaces

Perfect image of a metrizable space is metrizable.

$\mathbb R^{\omega}$ in the box topology not paracompact?

Does normal space guarantees existence of normal cover

Why do we define partitions of unity to be locally finite instead of pointwise finite?

Help with proof of Lemma 1 in "A note on paracompact spaces" (Michael, PAMS 4 (5), 1953)

locally finite family $ \mathcal{A} $

show that every countable subcover is $\sigma$- locally finite refinement. (every regular Lindelöf space is paracompact)

Paracompactness of topological group.

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