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:
“We are closed in, and the key is turned
On our uncertainty;”
—William Butler Yeats (1865–1939)
“One might get the impression that I recommend a new methodology which replaces induction by counterinduction and uses a multiplicity of theories, metaphysical views, fairy tales, instead of the customary pair theory/observation. This impression would certainly be mistaken. My intention is not to replace one set of general rules by another such set: my intention is rather to convince the reader that all methodologies, even the most obvious ones, have their limits.”
—Paul Feyerabend (1924–1994)