\begin{definition}[Definition:Path (Topology)]
Let $T = \struct {S, \tau}$ be a topological space.
Let $I \subset \R$ be the closed real interval $\closedint a b$.
A '''path in $T$''' is a continuous mapping $\gamma: I \to S$.
The mapping $\gamma$ can be referred as:
:a '''path (in $T$) joining $\map \gamma a$ and $\map \gamma b$'''
or:
:a '''path (in $T$) from $\map \gamma a$ to $\map \gamma b$'''.
It is common to refer to a point $z = \map \gamma t$ as a '''point on the path $\gamma$''', even though $z$ is in fact on the image of $\gamma$.
\end{definition}