Essential mapping
From Encyclopedia of Mathematics
A continuous mapping of a topological space
into an open simplex
such that every continuous mapping
that coincides with
at all points of the set
is a mapping onto the whole of
. For example, the identity mapping of
onto itself is an essential mapping.
References
[1] | P.S. Aleksandrov, B.A. Pasynkov, "Introduction to dimension theory" , Moscow (1973) (In Russian) |
Comments
Essential mappings are used to characterize the covering dimension (see Dimension) of normal spaces. A normal space has covering dimension if and only if it admits an essential mapping onto the
-dimensional simplex
.
References
[a1] | R. Engelking, "Dimension theory" , North-Holland & PWN (1978) |
How to Cite This Entry:
Essential mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Essential_mapping&oldid=34342
Essential mapping. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Essential_mapping&oldid=34342
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article