, Volume 32, Issue 3, pp 379-386

Localization of the degree on lower-dimensional sets

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The restriction of an essential mapping to the inverse image of a simplex of arbitrary dimension is still essential.

Received January 1986/Revised November 2003
This is an unmodified copy of a working paper (Mertens 1986), which was the basic tool of (Mertens 89, 91). Nowadays it is to some extent superseded by (Mertens 1992a), which, as shown in (Mertens 1992b), directly implies the “Small Worlds Axiom”, which itself is a very strong form of existence theorem. However, this latter route is limited to fields of coefficients, instead of arbitrary modules like here, and hence would not support the whole discussion in Mertens (89, 91) in terms of “(M,M’)-stability” etc. Further, the approach here may appear more intuitive and geometric to many readers than that in (Mertens 1992a).