\begin{definition}[Definition:Multiple Pointed Topology]
Let $T = \struct {S, \tau}$ be a topological space.
Let $A$ be a finite set whose cardinality is greater than $1$.
Let $D = \struct {A, \set {\O, A} }$ be the indiscrete space on $A$.
Let $T \times D$ be the product space of $T$ and $D$.
Then $T \times D$ is known as the '''multiple pointed topology''' on $T$.
It is seen that $T \times D$ is conceptually equivalent to taking the space $T$ and replacing each point with a finite set of topologically indistinguishable points.
\end{definition}