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Categorical length, relative L-S category and higher Hopf invariants

Norio Iwase (2009)

Banach Center Publications

In this paper we introduce the categorical length, a homotopy version of Fox categorical sequence, and an extended version of relative L-S category which contains the classical notions of Berstein-Ganea and Fadell-Husseini. We then show that, for a space or a pair, the categorical length for categorical sequences is precisely the L-S category or the relative L-S category in the sense of Fadell-Husseini respectively. Higher Hopf invariants, cup length, module weights, and recent computations by Kono...

Coincidence free pairs of maps

Ulrich Koschorke (2006)

Archivum Mathematicum

This paper centers around two basic problems of topological coincidence theory. First, try to measure (with the help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of coincidence free maps. Secondly, describe the set of loose pairs of homotopy classes. We give a brief (and necessarily very incomplete) survey of some old and new advances concerning the first problem. Then we attack the second problem mainly in the setting of homotopy...

Coincidence points and maximal elements of multifunctions on convex spaces

Sehie Park (1995)

Commentationes Mathematicae Universitatis Carolinae

Generalized and unified versions of coincidence or maximal element theorems of Fan, Yannelis and Prabhakar, Ha, Sessa, Tarafdar, Rim and Kim, Mehta and Sessa, Kim and Tan are obtained. Our arguments are based on our recent works on a broad class of multifunctions containing composites of acyclic maps defined on convex subsets of Hausdorff topological vector spaces.

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