cell attachment
Let X be a topological space,
and let Y be the adjunction
Y:=,
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 |