Question

Is the product of paracompact with $\sigma$-compact always paracompact?

score 64 · Answer 1 · 2021-08-19 01:03:26

64

Views

Is the product of paracompact with $\sigma$-compact always paracompact?

Published on 19 Aug 2021 - 1:03

score 655 · Answer 2 · 2021-10-10 08:14:26

655

Views

An Example for the Partition of Unity for a Circle

Published on 10 Oct 2021 - 8:14

score 323 · Answer 3 · 2021-10-10 10:35:14

323

Views

An Intuition for Paracompactness

Published on 10 Oct 2021 - 10:35

score 134 · Answer 4 · 2021-11-12 19:43:54

134

Views

If $X$ is paracompact then $f(X)$ not need to be paracompact

Published on 12 Nov 2021 - 19:43

score 71 · Answer 5 · 2021-11-16 06:18:07

71

Views

If a locally finite open cover has a locally finite closed refinement, it has a locally finite open barycentric refinement

Published on 16 Nov 2021 - 6:18

score 600 · Answer 6 · 2021-11-21 15:38:27

600

Views

An example of a non-paracompact topological space

Published on 21 Nov 2021 - 15:38

score 131 · Answer 7 · 2021-11-22 17:58:21

131

Views

Intersection of Open Set and Complement of Compact Set Is Open

Published on 22 Nov 2021 - 17:58

score 132 · Answer 8 · 2021-12-03 15:50:15

132

Views

Why is paracompactness needed to prove a regular space is normal?

Published on 03 Dec 2021 - 15:50

score 53 · Answer 9 · 2021-12-04 23:26:38

53

Views

countably locally finite and locally finite covers

Published on 04 Dec 2021 - 23:26

score 37 · Answer 10 · 2022-01-09 17:08:44

37

Views

Product of paracompact and compact spaces

Published on 09 Jan 2022 - 17:08

score 41 · Answer 11 · 2022-01-10 13:47:52

41

Views

In a $T_3$-space with $\sigma$-locally finite base, every open set is an $F_\sigma$ set.

Published on 10 Jan 2022 - 13:47

score 59 · Answer 12 · 2022-01-22 00:42:31

59

Views

Is the deleted total space of a vector bundle over a paracompact space paracompact?

Published on 22 Jan 2022 - 0:42

score 29 · Answer 13 · 2022-02-21 11:35:51

29

Views

How Regularity of $X$ implies $\mathcal {A}$ covers $X$?

Published on 21 Feb 2022 - 11:35

score 876 · Answer 14 · 2022-02-28 01:43:58

876

Views

Every closed subspace of a paracompact space $X$ is paracompact.

Published on 28 Feb 2022 - 1:43

score 46 · Answer 15 · 2022-03-05 11:48:45

46

Views

Does locally compact and paracompact imply $X\setminus E$ is contained in a countable union of compact sets, when $E$ has finite (Baire) measure?

Published on 05 Mar 2022 - 11:48

List Question

Is the product of paracompact with $\sigma$-compact always paracompact?

An Example for the Partition of Unity for a Circle

An Intuition for Paracompactness

If $X$ is paracompact then $f(X)$ not need to be paracompact

If a locally finite open cover has a locally finite closed refinement, it has a locally finite open barycentric refinement

An example of a non-paracompact topological space

Intersection of Open Set and Complement of Compact Set Is Open

Why is paracompactness needed to prove a regular space is normal?

countably locally finite and locally finite covers

Product of paracompact and compact spaces

In a $T_3$-space with $\sigma$-locally finite base, every open set is an $F_\sigma$ set.

Is the deleted total space of a vector bundle over a paracompact space paracompact?

How Regularity of $X$ implies $\mathcal {A}$ covers $X$?

Every closed subspace of a paracompact space $X$ is paracompact.

Does locally compact and paracompact imply $X\setminus E$ is contained in a countable union of compact sets, when $E$ has finite (Baire) measure?

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