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 subspace, of $X$.

Title	subspace topology
Canonical name	SubspaceTopology
Date of creation	2013-03-22 11:53:22
Last modified on	2013-03-22 11:53:22
Owner	djao (24)
Last modified by	djao (24)
Numerical id	8
Author	djao (24)
Entry type	Definition
Classification	msc 54B05
Classification	msc 15A66
Classification	msc 11E88
Synonym	relative topology
Defines	topological subspace
Defines	subspace