Category:Fortissimo Space

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This category contains results about Fortissimo Space.

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.