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Descriptive Set Theory is the study of definable subsets of Polish spaces, where definable is taken to mean from the Borel or projective hierarchies. Other topics include infinite games and determinacy, definable equivalence relations and Borel reductions between them, Polish groups, and effective descriptive set theory.

3 votes

What are the names of the following classes of topological spaces?

For (1), $\omega$ bounded. I'm unaware of names for the other concepts.
Steven Clontz's user avatar
1 vote
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Almost compact sets

I don't specifically recall "almost compact" in the literature, but it's quite natural as it relates to "almost Menger" and "almost Lindelof". In general, relative compactness is not equivalent to a s …
Steven Clontz's user avatar