THE LOCALLY FINITE HYPERTOPOLOGY AND GENERALIZED UNIFORMITIES

Beer, Himmelberg, Prikry and Van Vleck showed that if X is a metrizable space, then the locally finite topology on 2X is the sup of all Hausdorff metric topologies on 2X generated by compatible metrics on X. The second author and Sharma generalized this result to normal spaces. In this paper it is s...

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Bibliographic Details
Published in:Zbornik radova Filozofskog fakulteta u Nišu. Serija Matematika 1991-01, Vol.5, p.113-116
Main Authors: Di Maio, Giuseppe, Naimpally, Somashekhar
Format: Article
Language:English
Subjects:
Finite spaces
General topology
Topological spaces
Uniformity
Online Access:Get full text
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Summary:Beer, Himmelberg, Prikry and Van Vleck showed that if X is a metrizable space, then the locally finite topology on 2X is the sup of all Hausdorff metric topologies on 2X generated by compatible metrics on X. The second author and Sharma generalized this result to normal spaces. In this paper it is shown that the locally finite topology on 2X is the Hausdorff generalized uniform topology corresponding to a generalized uniformity on X which is Mozzocchi as well as local. Neka Je 2X skup svih nepraznih zatvorenih podskupova datog topološkog prostora X. U radu se pokazuje da na svakom potpuno regularnom prostoru X postoji generalisana uniformnost koja je lokalna i Mozzocchijeva i takva da njom generisana uopštena Hausdorffova uniformnost na 2X indukuje lokalno konačnu topologiju na 2X.
ISSN:0353-1325