Fort space

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A Fort space 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:

• 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 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

[edit] See also

• Arens-Fort space

[edit] References

• M. K. Fort, Jr. "Nested neighborhoods in Hausdorff spaces." American Mathematical Monthly vol.62 (1955) 372.
• Lynn Arthur Steen and J. Arthur Seebach, Jr., Counterexamples in Topology. Springer-Verlag, New York, 1978. Reprinted by Dover Publications, New York, 1995. ISBN 048668735X (Dover edition).