Topologies on Hyperspaces1

Georgiou, Dimitris N.. "Topologies on Hyperspaces1." Bollettino dell'Unione Matematica Italiana 5.1 (2012): 173-186. <http://eudml.org/doc/290899>.

@article{Georgiou2012,
abstract = {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 $X$.},
author = {Georgiou, Dimitris N.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {173-186},
publisher = {Unione Matematica Italiana},
title = {Topologies on Hyperspaces1},
url = {http://eudml.org/doc/290899},
volume = {5},
year = {2012},
}

TY - JOUR
AU - Georgiou, Dimitris N.
TI - Topologies on Hyperspaces1
JO - Bollettino dell'Unione Matematica Italiana
DA - 2012/2//
PB - Unione Matematica Italiana
VL - 5
IS - 1
SP - 173
EP - 186
AB - 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 $X$.
LA - eng
UR - http://eudml.org/doc/290899
ER -