\begin{definition}[Definition:Component (Topology)]
Let $T = \left({S, \tau}\right)$ be a topological space.
Let the relation $\sim $ be defined on $T$ as follows:
:$x \sim y$ {{iff}} $x$ and $y$ are connected in $T$.
That is, {{iff}} there exists a connected set of $T$ that contains both $x$ and $y$.
\end{definition}