Interactive Real Analysis

An open set S is called disconnected if there are two open, non-empty sets U and V such that:

1. U V = 0
2. U V = S

A set S (not necessarily open) is called disconnected if there are two open sets U and V such that

1. (U S) # 0 and (V S) # 0
2. (U S) (V S) = 0
3. (U S) (V S) = S

If S is not disconnected it is called connected.