Recent content by hnbc1

Hi micromass, I'm not required to find spaces that are neither open nor closed, but the subsets of the two metrics spaces mentioned. We can pick any point x in Rn or Cn, construct an open ball which is an open set, and pick another point on the boundary or out of the boundary, and the union of...

Homework Statement 1. Find an uncountable number of subsets of metric spaces \left(\mathbb{R}^{n},d_{p}\right) and \left(\mathbb{C}^{n},d_{p}\right) that are neither open nor closed. 2. If 1\leq p<q , then the unit ball in \left(\mathbb{R}^{n},d_{p}\right) is contained in the unit ball in...

I think so.

Thanks, lanedance. I think the idea is pretty straightforward, but I need more efforts to prove it. I'll figure it out, thank you!

I need to show that the by eliminating infinitely many terms of the harmonic series, the remaining subseries can be made to converge to any positive real numbers. I have no clue to prove this. I know harmonic series diverges really slowly, will this fact come into play? Thank you very much!