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...
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...
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)...