Question

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

score 65 · Answer 1 · 2026-02-23 08:25:57

65

Views

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

Published on 23 Feb 2026 - 8:25

score 656 · Answer 2 · 2026-02-23 08:28:32

656

Views

An Example for the Partition of Unity for a Circle

Published on 23 Feb 2026 - 8:28

score 324 · Answer 3 · 2026-02-23 08:21:48

324

Views

An Intuition for Paracompactness

Published on 23 Feb 2026 - 8:21

score 135 · Answer 4 · 2026-02-23 08:25:56

135

Views

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

Published on 23 Feb 2026 - 8:25

score 72 · Answer 5 · 2026-02-23 08:27:43

72

Views

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

Published on 23 Feb 2026 - 8:27

score 601 · Answer 6 · 2026-02-23 08:24:26

601

Views

An example of a non-paracompact topological space

Published on 23 Feb 2026 - 8:24

score 132 · Answer 7 · 2026-02-23 08:23:28

132

Views

Intersection of Open Set and Complement of Compact Set Is Open

Published on 23 Feb 2026 - 8:23

score 133 · Answer 8 · 2026-02-23 08:22:50

133

Views

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

Published on 23 Feb 2026 - 8:22

score 54 · Answer 9 · 2026-02-23 08:25:53

54

Views

countably locally finite and locally finite covers

Published on 23 Feb 2026 - 8:25

score 38 · Answer 10 · 2026-02-23 08:24:59

38

Views

Product of paracompact and compact spaces

Published on 23 Feb 2026 - 8:24

score 42 · Answer 11 · 2026-02-23 08:27:02

42

Views

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

Published on 23 Feb 2026 - 8:27

score 60 · Answer 12 · 2026-02-23 08:24:23

60

Views

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

Published on 23 Feb 2026 - 8:24

score 30 · Answer 13 · 2026-02-23 08:28:34

30

Views

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

Published on 23 Feb 2026 - 8:28

score 877 · Answer 14 · 2026-02-23 08:25:21

877

Views

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

Published on 23 Feb 2026 - 8:25

score 47 · Answer 15 · 2026-02-23 08:27:47

47

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 23 Feb 2026 - 8:27

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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