cell attachment

Let X be a topological spaceMathworldPlanetmath, and let Y be the adjunctionPlanetmathPlanetmath Y:=XφDk, where Dk is a closed k-ball (http://planetmath.org/StandardNBall) and φ:Sk-1X is a continuous map, with Sk-1 is the (k-1)-sphere considered as the boundary of Dk. Then, we say that Y is obtained from X by the attachment of a k-cell, by the attaching map φ. The image ek of Dk in Y is called a closed k-cell, and the image ek of the interior


of Dk is the corresponding open k-cell.

Note that for k=0 the above definition reduces to the statement that Y is the disjoint unionMathworldPlanetmathPlanetmath of X with a one-point space.

More generally, we say that Y is obtained from X by cell attachment if Y is homeomorphicMathworldPlanetmath to an adjunction X{φi}Dki, where the maps {φi} into X are defined on the boundary spheres of closed ballsPlanetmathPlanetmath {Dki}.

Title cell attachment
Canonical name CellAttachment
Date of creation 2013-03-22 13:25:53
Last modified on 2013-03-22 13:25:53
Owner yark (2760)
Last modified by yark (2760)
Numerical id 13
Author yark (2760)
Entry type Definition
Classification msc 54B15
Synonym cell adjunction
Related topic CWComplex
Defines cell
Defines open cell
Defines closed cell
Defines attaching map