Recent content by metder

  1. M

    How Does the Function f(x) Demonstrate the Normality of a Metric Space?

    Homework Statement Let (X, d) be a metric space and let A,B\subsetX be two disjoint closed sets. Show that X is normal by using the function f(x)=d(x,A)/[d(X,A)+d(x,B)] The Attempt at a Solution I'm somewhat stuck on this. I'm guessing the proof is pretty short, but any help would be...
  2. M

    Proving Continuity of g: C0([0, 1]) x [0, 1]-->R

    Yeah, you're right. I was over thinking the problem. Thanks for the help.
  3. M

    Proving Continuity of g: C0([0, 1]) x [0, 1]-->R

    Homework Statement Let C0([0, 1]) be the set of continuous functions on the interval [0, 1] with the supremum topology. Prove that the map given by g: C0([0, 1]) x [0, 1]-->R given by g(f, a) = f(a) is continuous. The Attempt at a Solution I was originally thinking that maybe I could use...
  4. M

    Graduate Is the Closed Unit Square Homeomorphic to the Closed Unit Disc?

    I realize this is a classic problem, but I'm not sure exactly how to start on it: Show that the closed unit square region is homeomorphic to the closed unit disc.
  5. M

    Diagonalizable Proof Homework: True or False?

    Homework Statement Let V be the space of n X n matrices over F. Let A be a fixed n X n matrix over F. Let T and U be the linear operators on V defined by T(B) = AB U(B) = AB - BA. 1. True or false? If A is diagonalizable (over F), then T is diagonalizable. 2. True or false? If A is...