Fort space

In mathematics, Fort space, named after M. K. Fort, Jr., is an example in the theory of topological spaces.

Let X be an infinite set of points, of which P is one. Then a Fort space is defined by X together with all subsets A such that:

X is homeomorphic to the one-point compactification of a discrete space.

Modified Fort space is similar but has two particular points P and Q. So a subset is declared "open" if:

Fortissimo space is defined as follows. Let X be an uncountable set of points, of which P is one. A subset A is declared "open" if: