Recent content by christianrhiley

  1. C

    Graduate Is the Quotient Space X/Y Hausdorff When X is Locally Compact?

    Problem: Let X be a locally compact Hausdorff space, Y a subspace. Show that the quotient space X/Y is a Hausdorff space. My attempt at a solution: I don't have a solution. I cannot connect a Hausdorff space with a quotient space. Since X is compact Hausdorff x,y \in X s.t. x and y can...
  2. C

    Real Analysis Question regarding Series

    Solved It! Solved It!
  3. C

    Real Analysis Question regarding Series

    Homework Statement Let {a_n} be a monotonically decreasing sequence of positive real numbers with lim a_n = 0. Show the radius of convergence of \suma_nx^{}n is at least 1. The Attempt at a Solution I have no real attempt at a solution since I'm unsure how to proceed. I've tried using...
  4. C

    Are Sequence Definitions for Bounded Sequences Adequate for Proving Boundedness?

    Definitions: Let {x[n]} be a bounded sequence in Reals. We define {y[k]} and {z[k]} by y[k]=sup{x[n]: n \geq k}, z[k]=inf{x[n]: n \geq k} Claim: (i) Both y[k] and z[k] are bounded sequences (ii){y[k]} is a decreasing sequence (iii){z[k]} is an increasing sequence Proof: (i)...