Definition:Connected (Topology)/Points

Definition
Let $T = \struct {S, \tau}$ be a topological space.

Let $a, b \in S$.

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

Also see

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