topological sum

Given two topological spacesMathworldPlanetmath X and Y, their topological sum is defined to be the set XY (see the entry disjoint unionMathworldPlanetmathPlanetmath) equipped with the finest topology such that the inclusion mapsMathworldPlanetmath from X and Y into XY are continuousPlanetmathPlanetmath. A basis for this topology consists of the union of the set of open subsets of X and the set of open subsets of Y.

Title topological sum
Canonical name TopologicalSum
Date of creation 2013-03-22 14:41:29
Last modified on 2013-03-22 14:41:29
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 7
Author rspuzio (6075)
Entry type Definition
Classification msc 54A99
Synonym coproductMathworldPlanetmath in the category of topological spaces
Synonym topological disjoint union