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Topological Algebra and its Applications

Ed. by Sanchis, Manuel

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Mathematical Citation Quotient (MCQ) 2016: 0.20


Emerging Science

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2299-3231
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Kuratowski Monoids of n-Topological Spaces

Taras Banakh
  • Corresponding author
  • Ivan Franko National University of Lviv, Universytatska 1, 79000, Lviv, Ukraine
  • Institute of Mathematics, Jan Kochanowski University, Swietokrzyka 15, Kielce, Poland
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  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Ostap Chervak / Tetyana Martynyuk / Maksym Pylypovych / Alex Ravsky
  • Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of National Academy of Sciences, Naukova 3b, Lviv, Ukraine
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Markiyan Simkiv
Published Online: 2018-03-28 | DOI: https://doi.org/10.1515/taa-2018-0001

Abstract

Generalizing the famous 14-set closure-complement Theorem of Kuratowski from 1922, we prove that for a set X endowed with n pairwise comparable topologies Ʈ1 ⊂ · · · ⊂ Ʈn, by repeated application of the operations of complement and closure in the topologies Ʈ1, . . . , Ʈn to a subset A ⊂ X we can obtain at most

Keywords: Kuratowski monoid; polytopological space; n-topological space

MSC 2010: 54A10; 54E55; 54H10; 06F05

References

  • [1] A.V.Chagrov, Kuratowski Numbers, in: Application of functional analysis in approximation theory, Kalinin Gos. Univ., Kalinin (1982), 186-190.Google Scholar

  • [2] B.J. Gardner, M. Jackson, The Kuratowski Closure-Complement Theorem, New Zealand J. Math. 38 (2008), 9-44.Google Scholar

  • [3] R. Graham, D. Knuth, O. Patashnik, Concrete mathematics. A foundation for computer science, Addison-Wesley Publishing Company, Reading, MA, 1994.Google Scholar

  • [4] K. Kuratowski, Sur l’opération A de l’Analysis Situs, Fund. Math. 3 (1922) 182-199.Google Scholar

  • [5] S. Plewik, M. Walczynska, The monoid consisting of Kuratowski operations, J. Math. 2013, Art. ID 289854, 9 pp.Google Scholar

  • [6] J. Shallit, R. Willard, Kuratowski’s Theorem for two closure operators, preprint (arXiv:1109.1227).Google Scholar

  • [7] D. Sherman, Variations on Kuratowski’s 14-set theorem, Amer. Math. Monthly, 117:2 (2010), 113-123.Google Scholar

About the article

Received: 2017-03-30

Accepted: 2018-01-30

Published Online: 2018-03-28


Citation Information: Topological Algebra and its Applications, Volume 6, Issue 1, Pages 1–25, ISSN (Online) 2299-3231, DOI: https://doi.org/10.1515/taa-2018-0001.

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© 2018. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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