Recent content by Xian'an Jin

  1. X

    For help, A simple question about topology

    What is a Jordan curve Let C be the circle x^2+y^2=1 in R^2, f is continuous bijection from R^2 to R^2, is f(C) a Jordan curve? and what is a Jordan curve? what is its definiton?
  2. X

    For help, A simple question about topology

    In calculus it's usually proved that a continuous bijection f:R->R is a homeomorphism. I think it can be proved by the following steps: step 1: show that f is monotone setp 2: a monotone continuous function has continouse inverse. Is the sketch of proof right? and can you provide a...
  3. X

    For help, A simple question about topology

    I know it, a contiunous bijection with a compact domain and a Hausdorff range is a homeomorphism. Unfortunately, here R^3 is not compact.
  4. X

    For help, A simple question about topology

    Is a continuous 1-1 and onto mapping from the Euclidean 3-space to itself a homeomorphism? i.e. Is its inverse also continous?
Back
Top