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:
“‘Tis said of love that it sometimes goes, sometimes flies; runs with one, walks gravely with another; turns a third into ice, and sets a fourth in a flame: it wounds one, another it kills: like lightning it begins and ends in the same moment: it makes that fort yield at night which it besieged but in the morning; for there is no force able to resist it.”
—Miguel De Cervantes (1547–1616)
“To play is nothing but the imitative substitution of a pleasurable, superfluous and voluntary action for a serious, necessary, imperative and difficult one. At the cradle of play as well as of artistic activity there stood leisure, tedium entailed by increased spiritual mobility, a horror vacui, the need of letting forms no longer imprisoned move freely, of filling empty time with sequences of notes, empty space with sequences of form.”
—Max J. Friedländer (1867–1958)