JournalspmVol. 70 / No. 3DOI 10.4171/pm/1931

Relations between minimal usco and minimal cusco maps

  • Ľubica Holá

    Academy of Sciences, Bratislava, Slovak Republic
  • Dušan Holý

    Trnavská univerzita v Trnave, Trnava, Slovak Republic
Relations between minimal usco and minimal cusco  maps cover

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Abstract

In our paper we give a characterization of (set-valued) maps which are minimal usco and minimal cusco simultaneously. Let be a topological space and be a Banach space. We show that there is a bijection between the space of minimal usco maps from to and the space of minimal cusco maps from to , and we study this bijection with respect to various topologies on underlying spaces. Let be a Baire space and be a Banach space. Then and are homeomorphic, where is the topology of uniform convergence.