JournalspmVol. 70, No. 3pp. 211–224

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 XX be a topological space and YY be a Banach space. We show that there is a bijection between the space MU(X,Y)\operatorname{MU}(X,Y) of minimal usco maps from XX to YY and the space MC(X,Y)\operatorname{MC}(X,Y) of minimal cusco maps from XX to YY, and we study this bijection with respect to various topologies on underlying spaces. Let XX be a Baire space and YY be a Banach space. Then (MU(X,Y),τU)(\operatorname{MU}(X,Y),\tau_U) and (MC(X,Y),τU)(\operatorname{MC}(X,Y),\tau_U) are homeomorphic, where τU\tau_U is the topology of uniform convergence.

Cite this article

Ľubica Holá, Dušan Holý, Relations between minimal usco and minimal cusco maps. Port. Math. 70 (2013), no. 3, pp. 211–224

DOI 10.4171/PM/1931