Displaying similar documents to “Conley index for set-valued maps: from theory to computation”

On the Schauder fixed point theorem

Lech Górniewicz, Danuta Rozpłoch-Nowakowska (1996)

Banach Center Publications

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The paper contains a survey of various results concerning the Schauder Fixed Point Theorem for metric spaces both in single-valued and multi-valued cases. A number of open problems is formulated.

On quadrirational Yang-Baxter maps.

Papageorgiou, V.G., Suris, Yu.B., Tongas, A.G., Veselov, A.P. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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Nielsen theory of transversal fixed point sets (with an appendix: C ∞ and C0 fixed point sets are the same, by R. E. Greene)

Helga Schirmer (1992)

Fundamenta Mathematicae

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Examples exist of smooth maps on the boundary of a smooth manifold M which allow continuous extensions over M without fixed points but no such smooth extensions. Such maps are studied here in more detail. They have a minimal fixed point set when all transversally fixed maps in their homotopy class are considered. Therefore we introduce a Nielsen fixed point theory for transversally fixed maps on smooth manifolds without or with boundary, and use it to calculate the minimum number of...

The Nielsen coincidence theory on topological manifolds

Jerzy Jezierski (1993)

Fundamenta Mathematicae

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We generalize the coincidence semi-index introduced in [D-J] to pairs of maps between topological manifolds. This permits extending the Nielsen theory to this class of maps.

The Vietoris system in strong shape and strong homology

Bernd Günther (1992)

Fundamenta Mathematicae

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We show that the Vietoris system of a space is isomorphic to a strong expansion of that space in the Steenrod homotopy category, and from this we derive a simple description of strong homology. It is proved that in ZFC strong homology does not have compact supports, and that enforcing compact supports by taking limits leads to a homology functor that does not factor over the strong shape category. For compact Hausdorff spaces strong homology is proved to be isomorphic to Massey's homology. ...