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.
|||P.S. Aleksandrov, B.A. Pasynkov, "Introduction to dimension theory" , Moscow (1973) (In Russian)|
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 .
|[a1]||R. Engelking, "Dimension theory" , North-Holland & PWN (1978)|
Essential mapping. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Essential_mapping&oldid=12470