4
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How to prove:

Cardinality of an infinite separable connected metric space is $2^{\aleph_0}$.

Thanks in advance!!

  • 0
    Do you know how to show a non-trivial connected metric space is uncountable?2012-09-21
  • 0
    my teacher gave me the same hint when i asked him, but i don't know really :(2012-09-21
  • 0
    The easiest proof I know uses Urysohn's lemma.2012-09-21
  • 0
    i know Urysohn's lemma2012-09-21

2 Answers 2