Definition:Fortissimo Space

Definition
Let $S$ be an uncountably infinite set.

Let $p \in S$ be a particular point of $S$.

Let $\tau_p \subseteq \mathcal P \left({S}\right)$ be a subset of the power set of $S$ defined as:
 * $\tau_p = \left\{{U \subseteq S: p \in \complement_S \left({U}\right)}\right\} \cup \left\{{U \subseteq S: \complement_S \left({U}\right)}\right.$ is countable (either finitely or infinitely)$\left.{}\right\}$

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 $T = \left({S, \tau_p}\right)$ is a Fortissimo space.

Also see

 * Fortissimo Topology is Topology

The name is a pun on Fort space.

The musical term forte means to be played loudly. The term fortissimo is a musical term meaning to be played very loudly.

So in a sense the term Fortissimo space can be thought of as being "like a Fort space, but more so."