| Title:
|
On the density of the hyperspace of a metric space (English) |
| Author:
|
Barbati, A. |
| Author:
|
Costantini, C. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
349-360 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
hyperspace |
| Keyword:
|
density |
| Keyword:
|
metric and metrizable space |
| Keyword:
|
Hausdorff metric hypertopology |
| Keyword:
|
locally finite hypertopology |
| Keyword:
|
GTB space |
| Keyword:
|
GK space |
| MSC:
|
54A25 |
| MSC:
|
54B20 |
| MSC:
|
54E35 |
| idZBL:
|
Zbl 0886.54007 |
| idMR:
|
MR1455502 |
| . |
| Date available:
|
2009-01-08T18:31:25Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118933 |
| . |
| Reference:
|
[1] Barbati A.: Strutture boreliane sull'iperspazio.Dissertation, Università degli Studi, Milano, 1992 Italian. |
| Reference:
|
[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. Zbl 0874.28016, MR 1326946 |
| Reference:
|
[3] Barbati A., Costantini C.: On a generalization of totally bounded and compact metric spaces.submitted for publication. Zbl 0919.54019 |
| Reference:
|
[4] Beer G.: Topologies on Closed and Closed Convex Sets.Kluwer Academic Publishers, Dordrecht, 1993. Zbl 0792.54008, MR 1269778 |
| Reference:
|
[5] Bella A., Costantini C.: On the Novak number of a hyperspace.Comment. Math. Univ. Carolinae 33 (1992), 695-698. Zbl 0782.54008, MR 1240191 |
| Reference:
|
[6] Easton W.B.: Powers of regular cardinals.Annals of Math. Logic 1 (1970), 139-178. Zbl 0209.30601, MR 0269497 |
| Reference:
|
[7] Engelking R.: General Topology, Revised and Completed Ed..Sigma series in pure mathematics, vol. 6, Heldermann, Berlin, 1989. MR 1039321 |
| Reference:
|
[8] Kunen K.: Set Theory. An Introduction to Independence Proofs.Studies in Logic, vol. 102, North-Holland, Amsterdam, 1980. Zbl 0534.03026, MR 0597342 |
| . |
