In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. In a topological space, a closed set can be defined as a set which contains all its limit points. In a complete metric space, a closed set is a set which is closed under the limit operation.
Read more about Closed Set: Equivalent Definitions of A Closed Set, Properties of Closed Sets, Examples of Closed Sets, More About Closed Sets
Famous quotes containing the words closed and/or set:
“Don: Why are they closed? They’re all closed, every one of them.
Pawnbroker: Sure they are. It’s Yom Kippur.
Don: It’s what?
Pawnbroker: It’s Yom Kippur, a Jewish holiday.
Don: It is? So what about Kelly’s and Gallagher’s?
Pawnbroker: They’re closed, too. We’ve got an agreement. They keep closed on Yom Kippur and we don’t open on St. Patrick’s.”
—Billy Wilder (b. 1906)
“Nothing in medieval dress distinguished the child from the adult. In the seventeenth century, however, the child, or at least the child of quality, whether noble or middle-class, ceased to be dressed like the grown-up. This is the essential point: henceforth he had an outfit reserved for his age group, which set him apart from the adults. These can be seen from the first glance at any of the numerous child portraits painted at the beginning of the seventeenth century.”
—Philippe Ariés (20th century)