Inessential mapping
homotopically-trivial mapping
A continuous mapping of a topological space
into the
-dimensional ball
such that there is a continuous mapping
that coincides with
on the inverse image
of the boundary
of
and takes
into
(that is,
). When
is a normal Hausdorff space, then
if and only if every continuous mapping
,
is inessential (Aleksandrov's theorem).
A continuous mapping of a topological space into the -dimensional sphere is called inessential if it is homotopic to the constant mapping.
Comments
The term "homotopically-trivial mapping" is not used in the context . See [a1], [a2] and [a3].
Generally, a mapping which is homotopic to a constant mapping is called nullhomotopic or homotopically trivial; in [a3] they are called inessential. See also Essential mapping.
References
[a1] | P.S. Aleksandrov, "Topologie" , 1 , Springer (1974) |
[a2] | R. Engelking, "Dimension theory" , PWN (1977) |
[a3] | W. Hurevicz, G. Wallman, "Dimension theory" , Princeton Univ. Press (1948) |
Inessential mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Inessential_mapping&oldid=40180