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On closure compatibility of ideal topological spaces and idempotency of the local closure function

Abstract

The aim of this paper is to continue the work started in Pavlović (Filomat 30(14):3725–3731, 2016) . We investigate further the properties of the local closure function and the spaces defined by it using common ideals, like ideals of finite sets, countable sets, closed and discrete sets, scattered sets and nowhere dense sets. Also, closure compatibility between the topology and the ideal, idempotency, and cases when the local closure of the whole space X is X or a proper subset of X, are closely investigated. In the case of closure compatibility and idempotency of the local closure function, the topology obtained by the local closure function is completely described.

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Acknowledgements

The authors acknowledge the financial support of the Ministry of Education, Science and Technological Development of the Republic of Serbia (Grant No. 451-03-68/2020-14/200125).

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Correspondence to Aleksandar Pavlović.

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Njamcul, A., Pavlović, A. On closure compatibility of ideal topological spaces and idempotency of the local closure function. Period Math Hung 84, 221–234 (2022). https://doi.org/10.1007/s10998-021-00401-1

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  • DOI: https://doi.org/10.1007/s10998-021-00401-1

Keywords

  • Ideal topological space
  • Local function
  • Local closure function
  • \(\theta \)-open sets
  • \(\theta \)-closure
  • Closure compatibility

Mathematics Subject Classification

  • 54A10
  • 54A05
  • 54B99
  • 54E99