5.3. Connected and Disconnected Sets
Definition 5.3.1: Connected and Disconnected
An open set S is called disconnected if there
are two open, non-empty sets U and V such that:
- U V = 0
- U V = S
A set S (not necessarily open) is called disconnected if there are two open sets U and V such that
- (U S) # 0 and (V S) # 0
- (U S) (V S) = 0
- (U S) (V S) = S
If S is not disconnected it is called connected.