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:
“How often we read that the enemy occupied a position which commanded the old, and so the fort was evacuated! Have not the school-house and the printing-press occupied a position which commands such a fort as this?”
—Henry David Thoreau (1817–1862)
“There is commonly sufficient space about us. Our horizon is never quite at our elbows.”
—Henry David Thoreau (1817–1862)