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:
“What I call middle-class society is any society that becomes rigidified in predetermined forms, forbidding all evolution, all gains, all progress, all discovery. I call middle-class a closed society in which life has no taste, in which the air is tainted, in which ideas and men are corrupt. And I think that a man who takes a stand against this death is in a sense a revolutionary.”
—Frantz Fanon (1925–1961)
“Well, most men have bound their eyes with one or another handkerchief, and attached themselves to some of these communities of opinion. This conformity makes them not false in a few particulars, authors of a few lies, but false in all particulars. Their every truth is not quite true. Their two is not the real two, their four not the real four; so that every word they say chagrins us and we know not where to set them right.”
—Ralph Waldo Emerson (1803–1882)