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Remarks on balls in metric spaces

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Abstract

In this article we discuss metric spaces in which closure of open balls are the corresponding closed balls, and interior of closed balls are the corresponding open balls. Moreover, we try to explore relationships between these two assertions.

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References

  1. Ahuja, G.C., T.D. Narang, and S. Trehan. 1977. Best approximation on convex sets in metric linear spaces. Mathematische Nachrichten 78: 125–130. https://doi.org/10.1002/mana.19770780110.

    Article  MathSciNet  MATH  Google Scholar 

  2. Artemiadis, N. 1965. A remark on metric spaces. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen A 68: 316–318.

    MathSciNet  MATH  Google Scholar 

  3. Blumenthal, L. M. 1977. Theory and Applications of Distance Geometry(Second Ed.). New York: Chelesa Publishing Company New York.

  4. Freese, R., G. Murphy, and E. Andalfte. 1989. Strict convexity in \(M\)-spaces. Journal of Geometry 34: 42–49. https://doi.org/10.1007/BF01224232.

    Article  MathSciNet  MATH  Google Scholar 

  5. Khalil, R. 1988. Best approximation in metric spaces. Proceedings of the American Mathematical Society 103 (2): 579–586. https://doi.org/10.1090/S0002-9939-1988-0943087-4.

    Article  MathSciNet  MATH  Google Scholar 

  6. Kiventidis, T. 1988. Some properties of the spheres in metric spaces. Indian Journal of Pure Applied Mathematics 19 (11): 1077–1080.

    MathSciNet  MATH  Google Scholar 

  7. Menger, K. 1928. Untersuchungen über allgemeine Metrik. Mathematische Annalen 100: 75–163. https://doi.org/10.1007/BF01448840.

    Article  MathSciNet  MATH  Google Scholar 

  8. Natanson, I.P. 1960. Theory of Functions of a Real Variable, vol. II. New York: Frederick Ungar Publishing Company.

    MATH  Google Scholar 

  9. Sastry, K.P.R., and S.V.R. Naidu. 1979. Convexity conditions in metric linear spaces. Mathematics Seminar Notes (Kobe University) 7 (2): 235–251.

    MathSciNet  MATH  Google Scholar 

  10. Vasil’ev, A. I. 1979. Chebychev sets and strong convexity of metric linear spaces. Mathematics Notes 25: 335–340. http://mi.mathnet.ru/eng/mz8328.

  11. Wong, J.S.W. 1966. Remarks on metric spaces. Indag. Math. (Proceedings) 69: 70–73.

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors are thankful to the learned referees for their useful comments and valuable suggestions leading to an improvement of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Guru Nanak Dev University, Amritsar, India

    Jitender Singh & T. D. Narang

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  1. Jitender Singh
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  2. T. D. Narang
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Correspondence to Jitender Singh.

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Communicated by Samy Ponnusamy.

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Singh, J., Narang, T.D. Remarks on balls in metric spaces. J Anal 29, 1093–1103 (2021). https://doi.org/10.1007/s41478-020-00297-z

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  • DOI: https://doi.org/10.1007/s41478-020-00297-z

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