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Completion of Standard Fuzzy Metric Space
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Volume 3, 2015
Issue 2 (April)
Pages: 19-25   |   Vol. 3, No. 2, April 2015   |   Follow on         
Paper in PDF Downloads: 20   Since Aug. 28, 2015 Views: 1644   Since Aug. 28, 2015
Jehad R. Kider, Department of Applied Science, University of Technology, Baghdad, Iraq.
In this paper we recall the definition of standard fuzzy metric spaces then we discuss several properties of this space after some illustrative examples where given. After that we show that the existence of a standard fuzzy metric space which is not completable. Here we prove that every completable standard fuzzy metric space admits a unique [up to F-isometric] completation.
Standard Fuzzy Metric Space, F-Bounded Set, Completable Standard Fuzzy Metric Space
Ereeg M. A., ʺ metric spaces and fuzzy set theoryʺ, J. Math. Anal. Appl. Vol.69, (1979)205-230.
George A. and Veeramani P.V., ʺ On some results in fuzzy metric Spacesʺ, Fuzzy Sets and Systems Vol.64,( 1994) 395-399.
Georg A. and Veeramani P. V, ʺSome theorems in fuzzy metric Spacesʺ, J. Fuzzy Math.Vol. 3,( 1995) 933–940.
George A. and Veeramani P. V, ʺOn some results of analysis for Fuzzy metric spacesʺ, Fuzzy Sets and Systems Vol.90, (1997)365–368.
Gregori V. and Romaguera S., ʺ Some properties of fuzzy Metric Spacesʺ, Fuzzy sets Systems, Vol.115, (2000)485-489.
Gregori V. and Romaguera S, ʺOn completion of fuzzy metric Spacesʺ, Fuzzy sets Systems, Vol.130,(2002) 399–404.
Gregori V. and Romaguera S, ʺCharacterizing completable fuzzy Metric Spacesʺ, Fuzzy Sets and Systems Vol.144 (3), (2004)411-420.
Gregori V. Romaguera S. and Sapen A. , ʺUniform continuity in Fuzzy Metric Spacesʺ, Rend. Istit. Mat. Univ. Trieste Vol.32 (2), (2001)81-88.
Kaleva O. and Seikkala S., ʺ On fuzzy metric spaces, Fuzzy Sets and Systems, Vol.12, (1984)215-229.
Kramosil I. and Michalek J., ʺ Fuzzy metric and statistical metric Spacesʺ, Kybernetika Vol.11,(1975)326–334.
Menger K. , ʺStatistical metricsʺ, Proc. Nat. Acad. Sci. Vol.28,(1942)535-537.
Mihet D. ,ʺ A Banach contraction theorem in fuzzy metric spaceʺ, Fuzzy sets and systems Vol.144(2004),431-439.
Rodriguez, J. and Romaguera, S. ʺThe Hausdorff Fuzzy metric on compactʺ, Fuzzy Sets and Systems Vol.147,(2004)273-283.
Sepena, A., ʺ A contribution to study of fuzzy metric spaceʺ, Appl. Gen. Topology Vol.2, (2001)63-76.
Schweizer, B. and Sklar A., ʺStatistical metric spacesʺ, PaciAc J. Math. Vol.10, (1960)314-334.
Veeramani P. V., ʺBest approximation in fuzzy metric spacesʺ, J. Fuzzy Math. Vol.9, (2001)75-80.
Kider J. R. "Compact Standard Fuzzy Metric Space", ijma Vol.5(7),(2014)129-136
Kreyzig E. "Introductory Functional Analysis With Applications", Wiley (1978) New York
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