connected set in a topological space

Let $Y$ be a topological space and $X\subseteq Y$ be given the subspace topology. We say that $X$ is connected iff we cannot find nonempty open sets $U,V\subseteq X$ such that $U\cap V=\mathrm{\varnothing }$ and $U\cup V=X$.

Title	connected set in a topological space
Canonical name	ConnectedSetInATopologicalSpace
Date of creation	2013-03-22 13:59:51
Last modified on	2013-03-22 13:59:51
Owner	ack (3732)
Last modified by	ack (3732)
Numerical id	6
Author	ack (3732)
Entry type	Definition
Classification	msc 54D05