We calculate the density of the hyperspace of a metric space, endowed with the Hausdorff or the locally finite topology. To this end, we introduce suitable generalizations of the notions of totally bounded and compact metric space.
@article{118933,
author = {Alberto Barbati and Camillo Costantini},
title = {On the density of the hyperspace of a metric space},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {38},
year = {1997},
pages = {349-360},
zbl = {0886.54007},
mrnumber = {1455502},
language = {en},
url = {http://dml.mathdoc.fr/item/118933}
}
Barbati, Alberto; Costantini, Camillo. On the density of the hyperspace of a metric space. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 349-360. http://gdmltest.u-ga.fr/item/118933/
Strutture boreliane sull'iperspazio, Dissertation, Università degli Studi, Milano, 1992 Italian.
The Hausdorff metric topology, the Attouch-Wets topology and the measurability of set-valued functions, Journal of Convex Analysis 1 (1994), 107-119. (1994) | MR 1326946 | Zbl 0874.28016
On a generalization of totally bounded and compact metric spaces, submitted for publication. | Zbl 0919.54019
Topologies on Closed and Closed Convex Sets, Kluwer Academic Publishers, Dordrecht, 1993. | MR 1269778 | Zbl 0792.54008
On the Novak number of a hyperspace, Comment. Math. Univ. Carolinae 33 (1992), 695-698. (1992) | MR 1240191 | Zbl 0782.54008
Powers of regular cardinals, Annals of Math. Logic 1 (1970), 139-178. (1970) | MR 0269497 | Zbl 0209.30601
General Topology, Revised and Completed Ed., Sigma series in pure mathematics, vol. 6, Heldermann, Berlin, 1989. | MR 1039321
Set Theory. An Introduction to Independence Proofs, Studies in Logic, vol. 102, North-Holland, Amsterdam, 1980. | MR 0597342 | Zbl 0534.03026