- #1
ehrenfest
- 2,020
- 1
Homework Statement
If U is open set in a topological space such that U = A union B, where A and B are disjoint, do both A and B have to both be open?
I think that they do not, but I cannot think of a counterexample...perhaps (-1,0) union [0,-1).
OK. That's a counterexample. So, now the question can both A and B not be open?