# Topological properties of the multifunction space $L(X)$ of Cusco maps

In: Mathematica Slovaca, vol. 58, no. 6
Ľubica Holá - Tanvi Jain - R. A. Mccoy

## Details:

Year, pages: 2008, 763 - 780
Keywords:
cusco maps, multifunction space, Vietoris topology, upper Vietoris topology, lower Vietoris topology, cardinal functions, metrizability, complete metrizability, countability properties
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 $x\in X$. We denote by $L(X)$, the space of all subsets $F$ of $X×\mathbb{R}$ such that $F$ is the graph of a cusco map from the space $X$ to the real line $\mathbb{R}$. In this paper, we study topological properties of $L(X)$ endowed with the Vietoris topology.
Holá, Ľ., Jain, T., Mccoy, R. 2008. Topological properties of the multifunction space $L(X)$ of Cusco maps. In Mathematica Slovaca, vol. 58, no.6, pp. 763-780. 0139-9918.
Holá, Ľ., Jain, T., Mccoy, R. (2008). Topological properties of the multifunction space $L(X)$ of Cusco maps. Mathematica Slovaca, 58(6), 763-780. 0139-9918.