Namespaces
Variants
Actions

Essential mapping

From Encyclopedia of Mathematics
Revision as of 16:59, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

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
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article