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Minimal uniformizability revisited in terms of normal sequence of covers

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Abstract

In this note, we further investigate minimal uniformizable spaces which is equivalent to minimal completely regular spaces due to Berri [3]. A new characterization of such spaces in terms of refinement of normally open covers has been given. Such a study is used to prove that a minimal uniformizable non-indiscrete space is pseudometrizable. When a subspace of a minimal uniformizable space is minimal uniformizable is also established.

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References

  1. C. K. Basu and S. S. Mandal, Chaos Solitons Fractals 42, 3242 (2009).

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  2. C. K. Basu and S. S. Mandal, in Real Analysis Exchange (Summer Symposium) (2010), p. 67.

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  3. M. P. Berri, Trans. Amer. Math. Soc. 108, 97 (1963).

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  4. S. Willard, General Topology (Addision-Wesley, Reading, Mass., 1970).

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Authors and Affiliations

  1. Department of Mathematics, West Bengal State University, Berunanpukuria, Malikapur, Barasat Kolkata, 700126, 24 Pgs. (N), West Bengal, India

    C. K. Basu

  2. Department of Mathematics, Krishnagar Women’s College, Krishnagar, 741001, Nadia, West Bengal, India

    S. S. Mandal

Authors
  1. C. K. Basu
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  2. S. S. Mandal
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Correspondence to C. K. Basu.

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Submitted by M. A. Malakhaltsev

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Basu, C.K., Mandal, S.S. Minimal uniformizability revisited in terms of normal sequence of covers. Lobachevskii J Math 36, 139–143 (2015). https://doi.org/10.1134/S1995080215020055

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  • DOI: https://doi.org/10.1134/S1995080215020055

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