Recent content by bertram

  1. B

    Is the Inverse Image of a Compact Set Always Bounded?

    Homework Statement Let f be a continuous mapping from metric spaces X to Y. K \subset Yis compact. Is f^{-1}(K) bounded? Homework Equations Theorem 4.8 Corollary (Rudin) A mapping f of a metric space X into Y is continuous iff f^{-1}(C) is closed in X for every closed set C in Y...
  2. B

    Continuity of f(x) at Rational and Irrational Points

    Homework Statement f(x) = {x^2 x \in Q -x^2 x \in R/Q At what points is f continuous? Homework Equations continuity: for every \epsilon > 0 there exists \delta > 0 d(f(x),f(p)) < \epsilon for all points x\inE for which d(x,p) < \delta The Attempt at a...