• Corpus ID: 211562617

COUNTABLE METRIC SPACES WITHOUT ISOLATED POINTS

@inproceedings{Dasgupta2005COUNTABLEMS,
  title={COUNTABLE METRIC SPACES WITHOUT ISOLATED POINTS},
  author={Abhijit Dasgupta},
  year={2005}
}
The theorem is remarkable, and gives some apparently counter-intuitive examples of spaces homeomorphic to the usual Q. Consider the “Sorgenfrey topology on Q,” which has the collection {(p, q] : p, q ∈ Q} as a base for its topology. This topology on Q is strictly finer than, and yet homeomorphic to, the usual topology of Q. Another example is Q×Q as a subspace of the Euclidean plane. In this article, we present three proofs of Sierpinski’s theorem. 
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