# Thread: Topology proof

1. ## Topology proof

Prove that S^(int), boundary of S and (S^c)^int are pairwise disjoint and their union is the entire Rn.

I understand that the set S is separate from it's boundary line then (S^c)^int is everything excluding the other two but how do I go about the proof?

2. ## Re: Topology proof

Let a point be in the intersection of 2 sets from those given. You'll get a contradiction (refer to the definitions of $S^{int}, \partial S$ and $(S^{c})^{int}$.