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. The Fort topology consists of X and all subsets A such that:

• A excludes P, or
• A contains all but a finite number of the points of X

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:

• A excludes P and Q, or
• A contains all but a finite number of the points of X

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:

• A excludes P, or
• A contains all but a countable set of the points of X

See also

• Arens–Fort space
• Appert topology
• Cofinite topology
• Excluded point topology

References

• M. K. Fort, Jr. "Nested neighborhoods in Hausdorff spaces." American Mathematical Monthly vol.62 (1955) 372.
• Steen, Lynn Arthur; Seebach, J. Arthur Jr. (1995) [1978], Counterexamples in Topology (Dover reprint of 1978 ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-486-68735-3, MR 0507446