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Countable space
Posted:
Nov 27, 2011 11:39 AM


Let S be a countable, 2nd countable, regular T0 space (equivalently, countable metrizable space). How to show that S embeds in the rationals?
Compare with the theorem: if S is a countable, 2nd countable, regular T0 space without isolated points (equivalently, perfect countable metrizable space) then S is homeomorphic to Q.
Are the proofs of these two theorems similar? Is the latter proof an extension or corollary of the former?



