- Thread starter
- #1

(1) Prove that every open set in R^n is the union of an at most countable collection of disjoint segments

Hint: You need to replace disjoint segments with the appropriate objects (which I'm thinking are open balls)

(2) Generalize the statement to a separable topological space

Hint: you may need some extra assumption

Any help would be much appreciated! The more detail, the better- thanks!