Selection theorems and minimal mappings in a cluster setting
type: Item
instance of: scholarly article
title: Selection theorems and minimal mappings in a cluster setting
zbMATH Open document ID: 1234.54027
DOI: 10.1216/RMJ-2011-41-3-851
author: Milan Matejdes
published in: Rocky Mountain Journal of Mathematics
publication date: 2011-08-02T00:00:00Z
review text: The domain space of the considered multifunctions is -- besides a topology -- endowed with a sort of path system \({\mathcal E}\) called here a cluster system. Using this additional structure \({\mathcal E}\) the notions of lower and upper \({\mathcal E}\)-continuity, \({\mathcal E}\)-cluster set, \({\mathcal E}\)-closedness of graph, are introduced and investigated. By using those concepts a unified treatment of closed graph theorems, continuous and quasicontinuous selectors and multiselectors and minimality of multifunctions is developed.
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 26E25
zbMATH DE Number: 5934873
zbMATH Keywords: set-valued function
zbMATH Keywords: \({\mathcal E}\)-continuity
zbMATH Keywords: cluster set
zbMATH Keywords: closed graph
zbMATH Keywords: quasicontinuity
zbMATH Keywords: selection
zbMATH Keywords: multiselection
zbMATH Keywords: minimal multifunction
reviewed by: Włodzimierz Ślęzak
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5934873