subspace topology

Let X be a topological spaceMathworldPlanetmath, and let YX be a subset. The subspace topology on Y is the topology whose open sets are those subsets of Y which equal UY for some open set UX.

In this context, the topological space Y obtained by taking the subspace topology is called a topological subspace, or simply subspaceMathworldPlanetmath, 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