Definition:Path-Connected/Topology/Points

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

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

That is, there exists a continuous mapping $f: \left[{0 \,.\,.\, 1}\right] \to X$ such that $f \left({0}\right) = a$ and $f \left({1}\right) = b$.

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