Questions tagged [paracompactness]

Question 1

I have a question about the proof of the following result in Kashiwara, Schapira, Sheaves on Manifolds: Proposition 2.5.12 [Let $X$ be a Hausdorff and locally compact space.] Let $A$ be a ring, and ...

Question 2

There are lots of questions about the upper separation properties, where people want to get open sets around infinite collections of closed sets. For example: construction of a discrete family ...

Question 3

It's known that $T_3$ Lindelof spaces are strongly paracompact, but I was wondering what sorts of conditions are needed to ensure strong paracompactness. For $T_3$ locally Lindelof spaces, ...

Question 4

If I have a paracompact Hausdorff topological space $X$, a closed subset $Y$ and an open set $U$ containing $Y$, why can we find a paracompact open set $V$ contained in $U$ such that $V$ still ...

Question 5

John Lee's Introduction to Topological Manifolds has, in its discussion of paracompactness: Lemma 4.74. Let $X$ be a topological space and $\mathcal{A}$ a collection of subsets of $X$. Then $\mathcal{...

Question 6

Is the following implication true for topological spaces? paracompact + perfectly normal $\implies$ hereditarily paracompact. A proof or references would be appreciated. Let $X$ be a topological ...

Question 7

There is a classic result by Chaber which says that a countably compact Hausdorff space with $G_\delta$ diagonal is metrizable. On Dan Ma's blog one can find that a countably compact space with $G_\...

Question 8

I'm studying the proof of the lemma that you can see in the image. It's usefull to prove a characterization of paracompactness. I'm trying to prove that if we have the additional hypothesis that $\...

Question 9

I am reading a paper on infinite-dimensional version of Sperner's Lemma and have a couple of clarification questions. This is Question 2. The author shows that an application of a Sperner's Lemma to ...

Question 10

Let $X$ be a topological space. $X$ is called paracompact if every open cover has a locally finite open refinement. (No separation axiom assumed here.) $X$ is called subparacompact if every open ...

Question 11

Reading e.g. https://arxiv.org/pdf/1606.01013 and https://arxiv.org/pdf/1012.0920 it seems that every Hausdorff scattered paracompact space is zero-dimensional. However, these articles typically cite ...

Question 12

Let $X$ be a topological space. A collection $\mathcal{A}$ of subsets of $X$ is said to be closure-preserving if for each subcollection $\mathcal{C}\subseteq \mathcal{A}$ we have that $$ \overline{ \...

Question 13

The Everywhere doubled line is an interesting example of a non-Hausdorff manifold that is homogeneous. See this question for some picture. The space can be described as the union of two real lines $X=...

Question 14

A family of subsets $\Omega$ of a topological space $X$ is locally ultimately dominating if for every $x \in X$ there is a neighbourhood $U^x$ such that $U^x \subseteq A$ for all but finitely many $A \...

Question 15

Since the Metrization Theorems are linked to the Paracompactness Theory, I recently wonder if there is some papers, books or theory written about the Metrization Theorems in terms of filters and nets ...

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Questions tagged [paracompactness]

Sections with compact support commutes with tensor over a locally compact Hausdorff space. Why can we reduce to the compact case?

Existence of Uncountable Discrete Family induced by Uncountable pw-disjoint Open Sets in a Metric Space

Conditions for Separable $T_{3\frac{1}{2}}$ Spaces to be Strongly Paracompact

Is there always a small paracompact open containing a closed set?

Locally Finite Iff Closures are Locally Finite

Is a paracompact perfectly normal space hereditarily paracompact?

Strongly collectionwise normal spaces with $G_\delta$ diagonal are submetrizable

Paracompactness and barycentric refinements

Regular cubical subdivision of the cube $[0, 1]^\omega$

Subparacompact spaces and paracompactness

Are all Hausdorff scattered paracompact spaces zero-dimensional?

Michael's sufficient condition for paracompactness in $T_1$ spaces

Is the Everywhere doubled line submetacompact?

Is a filter of type p contained in an ultrafilter of type p?

Filters and Nets on Metrization

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