Topologies on Hyperspaces1

Georgiou, Dimitris N.

Bollettino dell'Unione Matematica Italiana, Tome 5 (2012), p. 173-186 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

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 $X$ .

Publié le : 2012-02-01

MR 2919655 | Zbl 1259.54002

@article{BUMI_2012_9_5_1_173_0,
     author = {Dimitris N. Georgiou},
     title = {Topologies on Hyperspaces1},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5},
     year = {2012},
     pages = {173-186},
     zbl = {1259.54002},
     mrnumber = {2919655},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_1_173_0}
}

Georgiou, Dimitris N. Topologies on Hyperspaces1. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 173-186. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_1_173_0/

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