Given a topological spaceMathworldPlanetmath X, the cone on X (sometimes denoted by CX) is the quotient spaceMathworldPlanetmath X×[0,1]/X×{0}. Note that there is a natural inclusion XCX which sends x to (x,1).

If (X,x0) is a based topological spacePlanetmathPlanetmath, there is a similar reduced cone construction, given by X×[0,1]/(X×{0})({x0}×[0,1]). With this definition, the natural inclusion x(x,1) becomes a based map, where we take (x0,0) to be the basepoint of the reduced cone.

Title cone
Canonical name Cone
Date of creation 2013-03-22 13:25:20
Last modified on 2013-03-22 13:25:20
Owner antonio (1116)
Last modified by antonio (1116)
Numerical id 7
Author antonio (1116)
Entry type Definition
Classification msc 54B99
Related topic SuspensionMathworldPlanetmath
Related topic Join3
Defines reduced cone