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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

3 votes

Non-homeomorphic spaces that have continuous bijections between them

I don't have my copy of Kelley handy but I think in chapter 1 he gives the example where X is a countable disjoint union of open intervals and a countable discrete set while Y is a countable disjoint …
1 vote

Topological spaces that resemble the space of irrationals

Hello, Dan: Two countable dense subsets of the reals are order isomorphic and this extends to a homeomorphism of the reals. In particular, two countable dense subsets are homeomorphic via the restric …
ethan akin's user avatar