Definition:Fortissimo Space

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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.

Also see

  • Results about Fortissimo spaces can be found here.

Source of Name

This entry was named for Marion Kirkland Fort, Jr.

Linguistic Note

The name Fortissimo space 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.

As the term ultimately derives from a proper noun, that is the surname of Marion Kirkland Fort, Jr, the word Fortissimo when used in this context is capitalised.