Fort space

In mathematics, there are a few topological spaces named after M. K. Fort, Jr. Fort space[1] is defined by taking an infinite set X, with a particular point p in X, and declaring open the subsets A of X such that: The subspace

Modified Fort space[2] is similar but has two particular points.

So take an infinite set X with two distinct points p and q, and declare open the subsets A of X such that: The space X is compact and T1, but not Hausdorff.

Fortissimo space[3] is defined by taking an uncountable set X, with a particular point p in X, and declaring open the subsets A of X such that: The subspace

It is obtained by taking an uncountable discrete space, adding one point and defining a topology such that the resulting space is Lindelöf and contains the original space as a dense subspace.