Definition
A topological space is a set with a function
called the closure operator where is the power set of .
The closure operator has to satisfy the following properties for all
- (Extensivity)
- (Idempotence)
- (Preservation of binary unions)
- (Preservation of nullary unions)
If the second axiom, that of idempotence, is relaxed, then the axioms define a preclosure operator.
Read more about this topic: Kuratowski Closure Axioms
Famous quotes containing the word definition:
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)