On the topological transversality principle. (English) Zbl 0780.47048
The author proposes an axiomatic approach to the notion of topological essentiality [J. Dugundji and A. Granas, Fixed point theory, Vol. I (1982; Zbl 0483.47038)] in the spirit of H. Amann and S. A. Weiss [Math. Z. 130, 39-54 (1973; Zbl 0249.55004)]. He discusses the relation of his approach to topological degree theory and generalizes a result of H. Mönch [Nonlinear Anal., Theory Methods Appl. 4, 985-999 (1980; Zbl 0462.34041)] on fixed points of perturbations of linear Fredholm mappings of index zero.
Reviewer: C.Fenske (Gießen)
MSC:
| 47H11 | Degree theory for nonlinear operators |
| 54H25 | Fixed-point and coincidence theorems (topological aspects) |
| 55M25 | Degree, winding number |
Keywords:
topological transversality; essential mapping; continuation; topological essentiality; topological degree; fixed point; perturbations of linear Fredholm mappings of index zeroReferences:
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