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:
“Alas for the cripple Practice when it seeks to come up with the bird Theory, which flies before it. Try your design on the best school. The scholars are of all ages and temperaments and capacities. It is difficult to class them, some are too young, some are slow, some perverse. Each requires so much consideration, that the morning hope of the teacher, of a day of love and progress, is often closed at evening by despair.”
—Ralph Waldo Emerson (1803–1882)
“Don Pedro. But when shall we set the savage bull’s horns on the sensible Benedick’s head?
Claudio. Yes, and text underneath, “Here dwells Benedick, the married man?””
—William Shakespeare (1564–1616)