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=46293
Cellular mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Cellular_mapping&oldid=46293
This article was adapted from an original article by D.O. Baladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article