Let X be a topological spaceMathworldPlanetmath. Define a relationMathworldPlanetmath on X as follows: xy if there is no partition of X into disjoint open sets U and V such that UV=X, xU and yV.

This is an equivalence relationMathworldPlanetmath on X. The equivalence classesMathworldPlanetmath are called the quasicomponents of X.

Title quasicomponent
Canonical name Quasicomponent
Date of creation 2013-03-22 12:23:49
Last modified on 2013-03-22 12:23:49
Owner Evandar (27)
Last modified by Evandar (27)
Numerical id 4
Author Evandar (27)
Entry type Definition
Classification msc 54D05
Synonym quasi-component
Related topic ConnectedSpace
Related topic PathConnected
Related topic ConnectedComponent
Related topic PathComponent