Section of a mapping
From Encyclopedia of Mathematics
A mapping for which
. In a wider sense, a section of any morphism in an arbitrary category is a right-inverse morphism.
Comments
If is a subspace of
, a section over
of
is a mapping
such that
for all
. For a vector bundle
, where the mapping
is part of the structure defined, one speaks of a section of the vector bundle
rather than of a section of
. This applies, e.g., also to sheaves and fibrations. A standard notation for the set of sections in such a case is
, or
for the set of sections of
over
.
How to Cite This Entry:
Section of a mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Section_of_a_mapping&oldid=34521
Section of a mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Section_of_a_mapping&oldid=34521
This article was adapted from an original article by A.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article