cell attachment
Let be a topological space, and let be the adjunction , where is a closed -ball (http://planetmath.org/StandardNBall) and is a continuous map, with is the -sphere considered as the boundary of . Then, we say that is obtained from by the attachment of a -cell, by the attaching map The image of in is called a closed -cell, and the image of the interior
of is the corresponding open -cell.
Note that for the above definition reduces to the statement that is the disjoint union of with a one-point space.
More generally, we say that is obtained from by cell attachment if is homeomorphic to an adjunction , where the maps into are defined on the boundary spheres of closed balls .
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 |