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Topic: Countable space
Replies: 4   Last Post: Dec 1, 2011 11:30 AM

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Maarten Bergvelt

Posts: 2
Registered: 5/17/11
Countable space
Posted: Nov 27, 2011 11:39 AM
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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?

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