SubspaceTopology 2001-10-25 11:54:00 2003-03-13 23:46:22 Definition topological subspace subspace \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} \usepackage{xypic} Let $X$ be a topological space, and let $Y \subset X$ be a subset. The {\em 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 {\em topological subspace}, or simply {\em subspace}, of $X$.