User ethan akin - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-22T22:07:03Z http://mathoverflow.net/feeds/user/8286 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/30661/non-homeomorphic-spaces-that-have-continuous-bijections-between-them/35030#35030 Answer by ethan akin for Non-homeomorphic spaces that have continuous bijections between them ethan akin 2010-08-09T18:04:27Z 2010-08-09T18:04:27Z <p>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 union of left-closed, right-open intervals and a countable discrete set.The point is that you can get a half closed interval from an open one by attaching an endpoint and you can build an open interval using a sequence of half closed intervals. </p> http://mathoverflow.net/questions/33947/topological-spaces-that-resemble-the-space-of-irrationals/35027#35027 Answer by ethan akin for Topological spaces that resemble the space of irrationals ethan akin 2010-08-09T17:53:29Z 2010-08-09T17:53:29Z <p>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 restriction of a homeomorphism of the reals and this yields a homeomorphism of the complements. </p>