A subspaceMathworldPlanetmath A of a topological spaceMathworldPlanetmath X is called residual (or comeager) if and only if it is second category and its complement XA is first category. Equivalently, a set is residual if and only if it contains a countableMathworldPlanetmath intersectionMathworldPlanetmath of open ( dense sets.

Title residual
Canonical name Residual
Date of creation 2013-03-22 13:04:05
Last modified on 2013-03-22 13:04:05
Owner mps (409)
Last modified by mps (409)
Numerical id 7
Author mps (409)
Entry type Definition
Classification msc 54E52
Related topic BaireCategoryTheorem
Related topic SardsTheorem
Defines comeager