quasicomponent

Let $X$ be a topological space. Define a relation $\sim$ on $X$ as follows: $x\sim y$ if there is no partition of $X$ into disjoint open sets $U$ and $V$ such that $U\cup V=X$, $x\in U$ and $y\in V$.

This is an equivalence relation on $X$. The equivalence classes 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