Acta Mathematica Hungarica
Volume/Issue:
Volume 114: Issue 1-2
Quasi-uniform isomorphisms in fuzzy quasi-metric spaces, bicompletion and D -completion
Authors:
S. Romaguera Universidad Politécnica de Valencia E.T.S.I. Caminos, Departamento de Matemática Aplicada, IMPA-UPV 46071 Valencia Spain 46071 Valencia Spain

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A. Sapena Universidad Politécnica de Valencia Escuela Politécnica Superior de Gandia, IMPA-UPV 46730 Grau de Gandia, Valencia Spain 46730 Grau de Gandia, Valencia Spain

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O. Valero Universidad de las Islas Baleares Departamento de Ciencias Matemáticas e Informática 07122 Palma de Mallorca, Baleares Spain 07122 Palma de Mallorca, Baleares Spain

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Pages:
49–60
Online Publication Date:
22 Nov 2006
Publication Date:
01 Jan 2007
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10474-006-0512-z
Keywords:
fuzzy quasi-metric space; quasi-uniform space; quasi-uniform isomorphism; bicompletion; quiet; D -completion; balanced; 54A40; 54E15; 54D35; 54E35
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Abstract  

V. Gregori and S. Romaguera [17] obtained an example of a fuzzy metric space (in the sense of A. George and P. Veeramani) that is not completable, i.e. it is not isometric to a dense subspace of any complete fuzzy metric space; therefore, and contrary to the classical case, there exist quiet fuzzy quasi-metric spaces that are not bicompletable neither D-completable, via (quasi-)isometries. In this paper we show that, nevertheless, it is possible to obtain solutions to the problem of completion of fuzzy quasi-metric spaces by using quasi-uniform isomorphisms instead of (quasi-)isometries. Such solutions are deduced from a general method, given here, to obtain extension properties of fuzzy quasi-metric spaces from the corresponding ones of the classical theory of quasi-uniform and quasi-metric spaces.

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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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