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0
votes
2answers
180 views

Does locally compact plus pseudocompact imply paracompact?

This one is probably simple, but I don't see it yet. Is a locally compact, pseudocompact Hausdorff space necessarily paracompact?
1
vote
1answer
162 views

Characterisation of paracompact spaces by some sort of embeddability?

This question was inspired by this question. Before I start, I don't really mean embedding in what follows. I'm tempted to use plongement, for an exotic touch, but well, that's just a rose by another ...
4
votes
4answers
579 views

An example of a non-paracompact tvs (over the reals, say)

What is an example of a non-paracompact topological vector space? I'm aware of this question, but I don't care if my tvs is locally convex. In fact the wilder the better. The only criterion is that ...
18
votes
2answers
1k views

CW complexes and paracompactness

It seems like when we assume "niceness" in homotopy theory we assume that $X$ has the homotopy type of a CW complex, and in fiber bundle theory we assume that $X$ is paracompact. How do these two ...
2
votes
2answers
449 views

Conditions useful for proving paracompactness

I have a family of properties which I want to show taken together imply paracompactness (I can show that they are all implied by paracompactness). I can prove a whole bunch of things which are ...
3
votes
2answers
890 views

Paracompact but not Hausdorff

Do paracompact non-Hausdorff spaces admit partions of unity? I'm just curious.
6
votes
1answer
354 views

Countable paracompactness, normality and locally countable open covers

(repost from the topology Q&A board) I have a (T_1), Normal, countably paracompact space X. I would like to know if every locally countable open cover of X (i.e. an open cover such that every x ...
7
votes
2answers
679 views

Space whose product with paracompact space is paracompact

Is there a nice characterization of topological spaces with the property that the product with any paracompact space is paracompact? All compact spaces have this property (this can be shown from the ...
3
votes
1answer
164 views

Are mapping spaces paracompact?

Let X be a (finite dimensional) manifold. Consider smooth mapping space $$PX = C^\infty(I, X)$$ where I = [0,1] is the closed interval. Is this space paracompact? What if we fix a point x in X and ...
4
votes
4answers
1k views

Is the long line paracompact?

A manifold is usually defined as a second-countable hausdorff topological space which is locally homeomorphic to Rn. My understanding is that the reason "second-countable" is part of the definition is ...