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Homemorphism of two metric space

  1. Sep 11, 2014 #1
    If I create a bijective map between the open balls of two metric spaces, does that automatically imply that this map is a homemorphism?
     
  2. jcsd
  3. Sep 11, 2014 #2
    Yeah, it does (if I'm interpreting your statement correctly). You only need to check continuity on a basis, so if you have a bijection ##f: X \to Y## between two metric spaces and it is continuous on a basis for ##Y## and an open map on a basis for ## X## it's a homeomorphism.
     
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