# 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

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