In mathematics, Fort space, named after M. K. Fort, Jr.

M. K. Fort, Jr.

Marion Kirkland ‘Kirk’ Fort, Jr. was an American mathematician, specializing in general topology. The topological spaces called Fort space and Arens–Fort space are named after him....

, is an example in the theory of topological space

Topological space

Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, and continuity. They appear in virtually every branch of modern mathematics and are a central unifying notion...

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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:

• 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

Discrete space

In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points are "isolated" from each other in a certain sense.- Definitions :Given a set X:...

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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
  Excluded point topology
  In mathematics, the excluded point topology is a topology where exclusion of a particular point defines openness. Formally, let X be any set and p ∈ X. The collectionof subsets of X is then the excluded point topology on X....