Definition:Connected (Topology)/Points

Definition
Let $T = \left({S, \tau}\right)$ be a topological space.

Let $a, b \in S$.

Then $a$ and $b$ are connected (in $T$) iff there exists a connected set in $T$ containing both $a$ and $b$.

Also see

 * Equivalence of Definitions of Topological Connectedness for a series of equivalent definitions for connectedness.