Fuzzy quasi-metric spaces

Valentín Gregori

Spain

Universitat Politècnica de València

Salvador Romaguera

Spain

Universitat Politècnica de València

Departamento de Matemática Aplicada

Submitted: 2013-12-02

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Accepted: 2013-12-02

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DOI: https://doi.org/10.4995/agt.2004.2001
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Keywords:

Fuzzy quasi-metric space, Quasi-metric, Quasi-uniformity, Bi-complete, Isometry

Supporting agencies:

Generalitat Valenciana

grant GRUPOS 03/027

Abstract:

We generalize the notions of fuzzy metric by Kramosil and Michalek, and by George and Veeramani to the quasi-metric setting.We show that every quasi-metric induces a fuzzy quasi-metric and ,conversely, every fuzzy quasi-metric space generates a quasi-metrizable topology. Other basic properties are discussed.
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References:

A. Di Concilio, Spazi quasimetrici e topologie ad essi associate, Rend. Accad. Sci. Fis. Mat. Napoli 38 (1971), 113-130.

P. Fletcher, W.F. Lindgren, Quasi-Uniform Spaces, Marcel Dekker, New York, 1982.

A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7

A. George, P. Veeramani, Some theorems in fuzzy metric spaces, J. Fuzzy Math. 3 (1995), 933-940. https://doi.org/10.1016/0165-0114(94)90162-7

A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems 90 (1997), 365-368. https://doi.org/10.1016/S0165-0114(96)00207-2

V. Gregori, S. Romaguera, Some properties of fuzzy metric spaces, Fuzzy Sets and Systems 115 (2000), 485-489. https://doi.org/10.1016/S0165-0114(98)00281-4

V. Gregori, S. Romaguera, On completion of fuzzy metric spaces, Fuzzy Sets and Systems 130 (2002), 399-404. https://doi.org/10.1016/S0165-0114(02)00115-X

V. Gregori, S. Romaguera, Characterzing completable fuzzy metric spaces, Fuzzy Sets and Systems, to appear.

I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika 11 (1975), 326-334.

H.P.A. Künzi, Nonsymmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology, in: Handbook of the History of General Topology (eds. C.E. Aull and R. Lowen), vol. 3, Kluwer (Dordrecht, 2001), pp. 853-968. https://doi.org/10.1007/978-94-017-0470-0_3

D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems, to appear.

S. Salbany, Bitopological Spaces, Compactifications and Completions, Math. Monographs, no. 1, Dept. Math. Univ. Cape Town, 1974.

B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 314-334. https://doi.org/10.2140/pjm.1960.10.313

H. Sherwood, On the completion of probabilistic metric spaces, Z. Wahrsch. verw. Geb. 6 (1966), 62-64. https://doi.org/10.1007/BF00531809

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