here is one way how to write it as a set:
is continous, so
is closed for every
converges iff is a cauchy-sequence iff
this is in .
What is your solution?
I'm here again with another Royden question. The problem's pretty simple to state:
Given a sequence of real valued functions: where each is continuous and defined for all real numbers, show that
the set is an
I'm fairly certain that I've shown that the set is a . And I'm pretty sure that I can prove that every G-delta is an F-sigma-delta. This would mean I'm done. But wait! Wouldn't Royden have just asked me to prove it was a G-delta in the first place? By that logic, I think I did something wrong in my proof. Casn anyone lend a hand on this problem. (Or does asnyone think I'm right about the set being a g-delta?) Thanks for any responses. They will be diligently read.