Connected

Last updated Nov 1, 2022

Suppose $X$ is a Topological Space. We say $X$ is Connected if the only pair of Sets $U, V$ satisfying

1. $U, V$ Open
2. $U \cap V = \emptyset$
3. $U \cup V = X$

are $\emptyset, X$.

Suppose $X$ is a Topological Space and $S \subset X$. We say $S$ is Connected if it is a connected space when given the Subspace Topology.