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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
6
votes
Is a measurable homomorphism on a Lie group smooth?
Perhaps it is interesting to know that for group cocycles the answer is in general no (even up to coboundaries). For instance the extension $\mathbb{Z} \to \mathbb{R} \to S^1$ is described by a 2-cocy …
6
votes
Smooth classifying spaces?
Since classifying spaces for compact Lie groups are constructed via direct limits of Grassmanians, you can really put smooth structures on them, where with a smooth structure I mean the structure of a …