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

let $S$ and $T$ be two disjoint compact nonempty sets. Show that there are points $x_0$ in $S$ and a point $y_0$ in $T$ such that |$x$−$y$|≥|$x_0$−$y_0$| whenever $x$ is in $S$ and …

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 …

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. H …

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 ju …

Do paracompact non-Hausdorff spaces admit partions of unity? I'm just curious.

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 ca …

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 …

(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 …

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 thin …

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 …