Geodesic
Topologies on Hyperspaces1
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 1, pp. 173-186.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Let $Y$ and $Z$ be two arbitrary fixed topological spaces, $C(Y, Z)$ the set of all continuous maps from $Y$ to $Z$, and $\mathcal{O}_{Z}(Y)$ the set consisting of all open subsets $V$ of $Y$ such that $V = f^{-1}(U)$, where $f \in C(Y, Z)$ and $U$ is an open subset of $Z$. In this paper we continue the study of the $\mathcal{A}$-proper and $\mathcal{A}$-admissible topologies on $\mathcal{O}_{Z}(Y)$, where $\mathcal{A}$ is an arbitrary family of spaces, initiated in [6] and we offer new results concerning the finest $X$-proper topology $\tau(\{X\})$ on $\mathcal{O}_{Z}(Y)$ for several metrizable spaces $X$. 
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Georgiou, Dimitris N. Topologies on Hyperspaces1. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 1, pp. 173-186. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_1_a9/

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