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4
votes
0answers
454 views

continuous selection of a multivalued function?

The title is probably a bit too broad. I frequently encountered the following situation: suppose I need to select a solution to a linear equation from a compact set. Can I make this selection ...
3
votes
2answers
922 views

Paracompact but not Hausdorff

Do paracompact non-Hausdorff spaces admit partions of unity? I'm just curious.
62
votes
9answers
17k views

solving f(f(x))=g(x)

This question is of course inspired by the question How to solve f(f(x))=cosx and Joel David Hamkins' answer, which somehow gives a formal trick for solving equations of the form $f(f(x))=g(x)$ on a ...
4
votes
4answers
962 views

What is a reference for profinite sets?

The question is in the title. The motivation behind the question is as follows: there are plenty of references about profinite groups and profinite completions of groups. It seems that their not ...
50
votes
4answers
3k views

How do the compact Hausdorff topologies sit in the lattice of all topologies on a set?

This question is about the space of all topologies on a fixed set X. We may order the topologies by refinement, so that τ ≤ σ just in case every τ open set is open in σ. ...