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6
votes
Approximation of classifying space BG of compact Lie group G by finite CW complexes
Yes, but non-functorially in the compact Lie group $G$.
In 1951 Norman Steenrod produced the very first model [4, Theorem 19.6] of a $n$-universal space [4, Definition 19.2]. See the equivalence [4, …
4
votes
Dimensions of orbit spaces
The following statement is not quite the inequality that you want, but it is for more general spaces than orbifolds. (Note that so-called "good" orbifolds are the quotients of locally linear actions o …