Acta Mathematica Hungarica
Volume/Issue:
Volume 110: Issue 1-2
Pretopologies, preuniformities and probabilistic metric spaces
Authors:
M. Chicourrat Département de Mathématiques, Université Blaise Pascal 63177 Aubiére, France 63177 Aubiére, France

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C.D. Horváth Département de Mathématiques, Université de Perpignan 66860 Perpignan, Cedex, France 66860 Perpignan, Cedex, France

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Pages:
91–116
Online Publication Date:
14 Jan 2006
Publication Date:
13 Jan 2006
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-006-0009-9
Keywords:
pretopologies; preuniformities; semi-uniformities; Menger spaces; probabilistic metric spaces
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Summary  

A pretopology on a given set can be generated from a filter of reflexive relations on that set (we call such a structure a preuniformity). We show that the familly of filters inducing a given pretopology on Xform a complete lattice in the lattice of filters on X. The smallest and largest elements of that lattice are explicitly given. The largest element is characterized by a condition which is formally equivalent to a property introduced by Knaster--Kuratowski--Mazurkiewicz in their well known proof of Brouwer's fixed point theorem. Menger spaces and probabilistic metric spaces also generate pretopologies. Semi-uniformities and pretopologies associated to a possibly nonseparated Menger space are completely characterized.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632

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Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1950
Volumes
per Year		 3
Issues
per Year		 6
Founder Magyar Tudományos Akadémia  
Founder's
Address		 H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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