Physical Review D - Particles, Fields, Gravitation and Cosmology.
Vol. 80.
2009.

A study was conducted to demonstrate stability of coincidence points and set-valued covering maps in metric spaces. A set-valued map ψfrom X to Y was defined as a map sending each point x ε X to a non-empty closed subset ψ(x) of Y. The metric was defined in the Cartesian product X × Y by the formula φ = φx + φy. The set was called the graph of ψ and was denoted by gph(ψ), while a map was considered closed when its graph was closed. ψ was called a covering map when α > 0 existed for which ψ was an α-covering map. A set-valued map was also considered to be β-Lipschitz when it satisfied the Lipschitz condition with respect to the Hausdorff metric h with the constant β.

Authors

Arutyunov A.V.
^{1}

Journal

Number of issue

1

Language

English

Pages

555-557

Status

Published

Link

Volume

80

Year

2009

Organizations

^{1}Russian University of Peoples' Friendship, ul. Miklukho-Maklaya 6, Moscow 119198, Russian Federation

Keywords

Cartesian Products; Closed subsets; Coincidence points; Hausdorff metric; Lipschitz; Lipschitz conditions; Metric spaces; Set-valued map; Metric system; Topology; Set theory

Date of creation

19.10.2018

Date of change

19.10.2018

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Physical Review D - Particles, Fields, Gravitation and Cosmology.
Vol. 80.
2009.

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