Given a morphism in any category, a partial section of is a partial map such that equals the identity on the domain of . Explictly, this is a subobject of together with a morphism such that .
A local section of a continuous map is a partial section of whose domain is an open subset of .
In obstruction theory, one may be interested in how far one can construct a section of a bundle (say a principal bundle with group ), , over a CW-complex . Given a section of the restriction of over the -skeleton (i.e., a partial section of ), obstructions to extending to a partial section over are measured by a class in .
Last revised on September 4, 2013 at 02:21:36. See the history of this page for a list of all contributions to it.