Discrete Space

In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points are "isolated" from each other in a certain sense. The discrete topology is the finest topology that can be given on a set, i.e., it defines all subsets as open sets. In particular, each singleton is an open set in the discrete topology.

Read more about Discrete SpaceDefinitions, Properties, Uses, Indiscrete Spaces, Quotation

Other articles related to "discrete space, spaces, space, discrete":

Topological Manifold - Classification of Manifolds
... A 0-manifold is just a discrete space ... Such spaces are classified by their cardinality ... Every discrete space is paracompact ...
Discrete Space - Quotation
... Stanislaw Ulam characterized Los Angeles as "a discrete space, in which there is an hour's drive between points" ...
Baire Set - More General Definitions
... of a locally compact Hausdorff topological space is called a Baire set if it belongs to the smallest σ–ring containing all compact Gδ sets. 7.1), a subset of a topological space, X, is called a Baire set if it belongs to the smallest σ–algebra for which all continuous functions defined on X into the real line are ... A discrete topological space is locally compact and Hausdorff ...

Famous quotes containing the words space and/or discrete:

    Here were poor streets where faded gentility essayed with scanty space and shipwrecked means to make its last feeble stand, but tax-gatherer and creditor came there as elsewhere, and the poverty that yet faintly struggled was hardly less squalid and manifest than that which had long ago submitted and given up the game.
    Charles Dickens (1812–1870)

    One can describe a landscape in many different words and sentences, but one would not normally cut up a picture of a landscape and rearrange it in different patterns in order to describe it in different ways. Because a photograph is not composed of discrete units strung out in a linear row of meaningful pieces, we do not understand it by looking at one element after another in a set sequence. The photograph is understood in one act of seeing; it is perceived in a gestalt.
    Joshua Meyrowitz, U.S. educator, media critic. “The Blurring of Public and Private Behaviors,” No Sense of Place: The Impact of Electronic Media on Social Behavior, Oxford University Press (1985)