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Topological properties of the multifunction space L(X) of cusco maps
Authors:Ľ. Holá  Tanvi Jain  R. A. McCoy
Affiliation:(1) Academy of Sciences, Institute of Mathematics, Štefánikova 49, 81473 Bratislava, Slovakia;(2) Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, 110016, India;(3) Department of Mathematics, Virginia Tech, Blacksburg, VA 24060-0123, USA
Abstract:A set-valued mapping F from a topological space X to a topological space Y is called a cusco map if F is upper semicontinuous and F(x) is a nonempty, compact and connected subset of Y for each xX. We denote by L(X), the space of all subsets F of X × ℝ such that F is the graph of a cusco map from the space X to the real line ℝ. In this paper, we study topological properties of L(X) endowed with the Vietoris topology. The second author is supported by the SPM fellowship awarded by the Council of Scientific and Industrial Research, India.
Keywords:cusco maps  multifunction space  Vietoris topology  upper Vietoris topology  lower Vietoris topology  cardinal functions  metrizability  complete metrizability  countability properties
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