Recent content by jaymath

  1. J

    Subspaces of R^n Homotopy Equivalent But Not Homeomorphic

    Ah, okay, I was missing the fact that it need not be bijective, so as you say it can go anywhere.
  2. J

    Subspaces of R^n Homotopy Equivalent But Not Homeomorphic

    Im struggling with the argument. As I said I am working along the lines of balls homotopy equivalent to points. So for example in R^2 the closed unit disk is clearly not homemorphic to a single point, it fails as a bijection. But they are homotopy equivalent. But I can't see how there are...
  3. J

    Subspaces of R^n Homotopy Equivalent But Not Homeomorphic

    For each n in N give examples of subspaces of R^n, which are homotopy equivalent but NOT homeomorphic to each other. Give reasons for your answer. I'm working along the lines of open and closed intervals in R and balls in R^n with n>1. Although I'm struggling with the reasoning. Any...