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:
“She was so overcome by the splendor of his achievement that she took him into the closet and selected a choice apple and delivered it to him, along with an improving lecture upon the added value and flavor a treat took to itself when it came without sin through virtuous effort. And while she closed with a Scriptural flourish, he “hooked” a doughnut.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)
“Such a set of tittle tattle, prittle prattle visitants! Oh Dear! I am so sick of the ceremony and fuss of these fall lall people! So much dressing—chitchat—complimentary nonsense—In short, a country town is my detestation. All the conversation is scandal, all the attention, dress, and almost all the heart, folly, envy, and censoriousness.”
—Frances Burney (1752–1840)