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:
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“It’s a rare parent who can see his or her child clearly and objectively. At a school board meeting I attended . . . the only definition of a gifted child on which everyone in the audience could agree was “mine.””
—Jane Adams (20th century)
“One definition of man is “an intelligence served by organs.””
—Ralph Waldo Emerson (1803–1882)