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:
- 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
Famous quotes containing the words fort and/or space:
“There was a deserted log camp here, apparently used the previous winter, with its hovel or barn for cattle.... It was a simple and strong fort erected against the cold, and suggested what valiant trencher work had been done there.”
—Henry David Thoreau (18171862)
“It is the space inside that gives the drum its sound.”
—Hawaiian saying no. 1189, lelo NoEau, collected, translated, and annotated by Mary Kawena Pukui, Bishop Museum Press, Hawaii (1983)