On the density of the hyperspace of a metric space

Alberto Barbati; Camillo Costantini

Commentationes Mathematicae Universitatis Carolinae (1997)

  • Volume: 38, Issue: 2, page 349-360
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Barbati, Alberto, and Costantini, Camillo. "On the density of the hyperspace of a metric space." Commentationes Mathematicae Universitatis Carolinae 38.2 (1997): 349-360. <http://eudml.org/doc/248083>.

@article{Barbati1997,
abstract = {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.},
author = {Barbati, Alberto, Costantini, Camillo},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {hyperspace; density; metric and metrizable space; Hausdorff metric hypertopology; locally finite hypertopology; GTB space; GK space; hyperspace; density; totally bounded metric space},
language = {eng},
number = {2},
pages = {349-360},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the density of the hyperspace of a metric space},
url = {http://eudml.org/doc/248083},
volume = {38},
year = {1997},
}

TY - JOUR
AU - Barbati, Alberto
AU - Costantini, Camillo
TI - On the density of the hyperspace of a metric space
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1997
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 38
IS - 2
SP - 349
EP - 360
AB - 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.
LA - eng
KW - hyperspace; density; metric and metrizable space; Hausdorff metric hypertopology; locally finite hypertopology; GTB space; GK space; hyperspace; density; totally bounded metric space
UR - http://eudml.org/doc/248083
ER -

References

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  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. (1994) Zbl0874.28016MR1326946
  3. Barbati A., Costantini C., On a generalization of totally bounded and compact metric spaces, submitted for publication. Zbl0919.54019
  4. Beer G., Topologies on Closed and Closed Convex Sets, Kluwer Academic Publishers, Dordrecht, 1993. Zbl0792.54008MR1269778
  5. Bella A., Costantini C., On the Novak number of a hyperspace, Comment. Math. Univ. Carolinae 33 (1992), 695-698. (1992) Zbl0782.54008MR1240191
  6. Easton W.B., Powers of regular cardinals, Annals of Math. Logic 1 (1970), 139-178. (1970) Zbl0209.30601MR0269497
  7. Engelking R., General Topology, Revised and Completed Ed., Sigma series in pure mathematics, vol. 6, Heldermann, Berlin, 1989. MR1039321
  8. Kunen K., Set Theory. An Introduction to Independence Proofs, Studies in Logic, vol. 102, North-Holland, Amsterdam, 1980. Zbl0534.03026MR0597342

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