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Arabian Journal of Mathematics

, Volume 8, Issue 2, pp 125–132 | Cite as

Upper neighbours of Čech closure operators

  • T. KavithaEmail author
  • M. Kunheenkutty
  • P. T. Ramachandran
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Abstract

Here, we investigate the existence of upper neighbours in the lattice of \(T_{1}\) Čech closure operators on a fixed set. In this paper, we prove that a first countable \(T_{1}\) closure operator has no upper neighbour in the lattice of Čech closure operators.

Mathematics Subject Classification

54A05 03G10 

Notes

Acknowledgements

The authors express gratitude to the referee(s) and editor(s) for their valuable comments and suggestions which improved this paper. The first author acknowledges the financial support from U.G.C., Govt of India.

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Copyright information

© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • T. Kavitha
    • 1
    Email author
  • M. Kunheenkutty
    • 2
  • P. T. Ramachandran
    • 1
  1. 1.Department of MathematicsUniversity of CalicutCalicutIndia
  2. 2.CalicutIndia

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