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Basic question regarding continuous inverses

  1. Feb 3, 2009 #1
    Regarding the definition of homemorphism, when we say a function is a homeomorphism if it is continuous, bijective, and has a continuous inverse I assume that means over the codomain only.

    For example if we have a map from f: R -> (0,1) does f inverse need to be continuous on (0,1) only?
  2. jcsd
  3. Feb 3, 2009 #2


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    Well f inverse, if it exists, is only defined on (0,1). So it wouldn't make sense to require it to be continuous on a larger subset that (0,1).
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