Cellular mapping
From Encyclopedia of Mathematics
A mapping 
from one relative CW-complex 
into another 
such that 
, where 
and 
are the 
-skeletons of 
and 
relative to 
and 
, respectively. In the case when 
, one obtains a cellular mapping 
from the CW-complex 
into the CW-complex 
.
A homotopy 
, where 
, is called cellular if 
for all 
. The following cellular approximation theorem is the analogue of the simplicial approximation theorem (see Simplicial mapping): Let 
be a mapping from one relative CW-complex 
into another 
the restriction of which to some subcomplex 
is cellular. Then there exists a cellular mapping 
that is homotopic to 
relative to 
.
For references see also CW-complex.
Comments
References
| [a1] | E.H. Spanier, "Algebraic topology" , McGraw-Hill (1966) |
| [a2] | R. Brown, "Elements of modern topology" , McGraw-Hill (1968) |
| [a3] | C.R.F. Maunder, "Algebraic topology" , v. Nostrand (1970) pp. Section 7.5 |
How to Cite This Entry:
Cellular mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cellular_mapping&oldid=12612
Cellular mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cellular_mapping&oldid=12612
This article was adapted from an original article by D.O. Baladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article