Displaying similar documents to “Spherical maps”

Fixed points of set-valued maps with closed proximally ∞-connected values

Grzegorz Gabor (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Introduction Many authors have developed the topological degree theory and the fixed point theory for set-valued maps using homological techniques (see for example [19, 28, 27, 16]). Lately, an elementary technique of single-valued approximation (on the graph) (see [11, 1, 13, 5, 9, 2, 6, 7]) has been used in constructing the fixed point index for set-valued maps with compact values (see [21, 20, 4]). In [20, 4] authors consider set-valued...

Topological and approximation methods of degree theory of set-valued maps

Wojciech Kryszewski

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SummaryThe theory of topological degree of set-valued maps determined by morphisms, i.e. maps with values which are continuous images of almost acyclic sets, is presented, together with some of its applications.In the first part, morphisms defined on finite-dimensional Euclidean manifolds are considered and the integer-valued degree is introduced by means of the Eilenberg-Montgomery-Górniewicz method based on the Vietoris-Begle-Sklyarenko theorem and using the approach of Dold in terms...

Multi-invertible maps and their applications

Mirosław Ślosarski (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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In this article, we define multi-invertible, multivalued maps. These mappings are a natural generalization of r-maps (in particular, the singlevalued invertible maps). They have many interesting properties and applications. In this article, the multi-invertible maps are applied to the construction of morphisms and to the theory of coincidence.

Shape theory of maps.

Zvonko Cerin (1995)

Revista Matemática de la Universidad Complutense de Madrid

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We shall describe a modification of homotopy theory of maps which we call shape theory of maps. This is accomplished by constructing the shape category of maps HMb. The category HMb is built using multi-valued functions. Its objects are maps of topological spaces while its morphisms are homotopy classes of collections of pairs of multi-valued functions which we call multi-binets. Various authors have previously given other descriptions of shape categories of maps. Our description is...

Fixed point index theory for a class of nonacyclic multivalued maps

Zdzisław Dzedzej

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CONTENTS0. Introduction.....................................................................5I. Homology.........................................................................6II. Multivalued maps...........................................................11III. Chain approximations and index...................................15IV. Chain approximations of decompositions of maps........18V. Index of decompositions for compact polyhedra............26VI. Index of decompositions for compact...