Definition:Path-Connected/Topology/Points

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

Let $a, b \in S$ be such that there exists a path from $a$ to $b$.

That is, there exists a continuous mapping $f: \closedint 0 1 \to S$ such that:
 * $\map f 0 = a$

and:
 * $\map f 1 = b$

Then $a$ and $b$ are path-connected in $T$.

Also see

 * Path-Connectedness is Equivalence Relation