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Math Help - countable+discrete=separable?

  1. #1
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    countable+discrete=separable?

    Is every countable discrete set - separable? If yes, why? Thank you.
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  2. #2
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    Hi

    In such case, isn't the set itself a countable dense subset?
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  3. #3
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    Quote Originally Posted by georgel View Post
    Is every countable discrete set - separable? If yes, why? Thank you.

    Well yes, and in a rather trivial way: as every singleton is open, there exists a countable set of points (all the points of the space!) s.t. every open subset of the space contains at least one of these points...

    Tonio
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