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hyperspace; density; metric and metrizable space; Hausdorff metric hypertopology; locally finite hypertopology; GTB space; GK space
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.
[1] Barbati A.: Strutture boreliane sull'iperspazio. Dissertation, Università degli Studi, Milano, 1992 Italian.
[2] Barbati A., Beer G., Hess C.: The Hausdorff metric topology, the Attouch-Wets topology and the measurability of set-valued functions. Journal of Convex Analysis 1 (1994), 107-119. MR 1326946 | Zbl 0874.28016
[3] Barbati A., Costantini C.: On a generalization of totally bounded and compact metric spaces. submitted for publication. Zbl 0919.54019
[4] Beer G.: Topologies on Closed and Closed Convex Sets. Kluwer Academic Publishers, Dordrecht, 1993. MR 1269778 | Zbl 0792.54008
[5] Bella A., Costantini C.: On the Novak number of a hyperspace. Comment. Math. Univ. Carolinae 33 (1992), 695-698. MR 1240191 | Zbl 0782.54008
[6] Easton W.B.: Powers of regular cardinals. Annals of Math. Logic 1 (1970), 139-178. MR 0269497 | Zbl 0209.30601
[7] Engelking R.: General Topology, Revised and Completed Ed. Sigma series in pure mathematics, vol. 6, Heldermann, Berlin, 1989. MR 1039321
[8] Kunen K.: Set Theory. An Introduction to Independence Proofs. Studies in Logic, vol. 102, North-Holland, Amsterdam, 1980. MR 0597342 | Zbl 0534.03026
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