# subspace topology

Let $X$ be a topological space, and let $Y\subset X$ be a subset. The subspace topology on $Y$ is the topology whose open sets are those subsets of $Y$ which equal $U\cap Y$ for some open set $U\subset X$.

In this context, the topological space $Y$ obtained by taking the subspace topology is called a topological subspace, or simply , of $X$.

Title subspace topology SubspaceTopology 2013-03-22 11:53:22 2013-03-22 11:53:22 djao (24) djao (24) 8 djao (24) Definition msc 54B05 msc 15A66 msc 11E88 relative topology topological subspace subspace