Displaying similar documents to “Multi-valued maps of subsets of Euclidean spaces”

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.

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...

Spherical maps

Andrzej Dawidowicz (1987)

Fundamenta Mathematicae

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Automatic continuity of biseparating maps

Jesús Araujo, Krzysztof Jarosz (2003)

Studia Mathematica

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We prove that a biseparating map between spaces of vector-valued continuous functions is usually automatically continuous. However, we also discuss special cases when this is not true.

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...