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Topological Algebra and its Applications

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Kuratowski Monoids of n-Topological Spaces

Taras Banakh
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  • 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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  • 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
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/ Markiyan Simkiv
Published Online: 2018-03-28 | DOI: https://doi.org/10.1515/taa-2018-0001


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


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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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