A Lefschetz-type Coincidence Theorem
نویسنده
چکیده
A Lefschetz-type coincidence theorem for two maps f, g : X → Y from an arbitrary topological space to a manifold is given: Ifg = λfg, that is, the coincidence index is equal to the Lefschetz number. It follows that if λfg 6= 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. Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, IL 61801. e-mail: [email protected] Subject Classification: 55M20, 55H25.
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