# 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 $U\cap V=\emptyset$ and $U\cup V=X$.

Title connected set in a topological space ConnectedSetInATopologicalSpace 2013-03-22 13:59:51 2013-03-22 13:59:51 ack (3732) ack (3732) 6 ack (3732) Definition msc 54D05