Recent content by mathanon

Thank you! That definitely helps!

How do you find the interior points of a subset? I understand that a point is an interior point if there exists an epsilon neighborhood that is in the set, but I don't know how that would work with specific sets. Any hints?

Prove that for any collection {O[SIZE="1"]α} of open subsets of ℝ, \bigcap O[SIZE="1"]α is open. I did the following for the union, but I don't see where to go with the intersection of a set. Here's what I have so far: Suppose O[SIZE="1"]α is an open set for each x \ni A. Let O=...

Let A be a nonempty subset of R that is bounded above and let α=supA. Show that there exists a monotone increasing sequence {an} in A such that α=lim an. Can the sequence {an} be chosen to be strictly increasing?