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:
“Since time immemorial, one the dry earth, scraped to the bone, of this immeasurable country, a few men travelled ceaselessly, they owned nothing, but they served no one, free and wretched lords in a strange kingdom. Janine did not know why this idea filled her with a sadness so soft and so vast that she closed her eyes. She only knew that this kingdom, which had always been promised to her would never be her, never again, except at this moment.”
—Albert Camus 1013–1960, French-Algerian novelist, dramatist, philosopher. Janine in Algeria, in The Fall, p. 27, Gallimard (9157)
“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)