\begin{definition}[Definition:Fortissimo Space]
Let $S$ be an uncountably infinite set.
Let $p \in S$ be a particular point of $S$.
Let $\tau_p \subseteq \powerset S$ be a subset of the power set of $S$ defined as:
:$\tau_p = \leftset {U \subseteq S: p \in \relcomp S U}$ or $\set {U \subseteq S: \relcomp S U}$ is countable (either finitely or infinitely)$\rightset {}$
That is, $\tau_p$ is the set of all subsets of $S$ whose complement in $S$ either contains $p$ or is countable.
Then $\tau_p$ is a '''Fortissimo topology''' on $S$, and the topological space $T = \struct {S, \tau_p}$ is a '''Fortissimo space'''.
\end{definition}