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A Lefschetz-type coincidence theorem

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Saveliev P.

Fundamenta Mathematicae

1999

tom 162

nr 1

65-89

A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: $I_{fg} = λ _{fg}$, that is, the coincidence index is equal to the Lefschetz number. It follows that if $λ_{fg} ≠ 0$ then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with "point-like" (acyclic) and "sphere-like" values.

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1 Fundamenta Mathematicae

1 Saveliev P.

1 1999

Wyniki wyszukiwania

A Lefschetz-type coincidence theorem