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Lobachevskii Journal of Mathematics

, Volume 39, Issue 9, pp 1446–1452 | Cite as

T0-Closure Operators and Pre-Orders

  • B. VenkateswarluEmail author
  • U. M. Swamy
Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
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Abstract

It is well known that the lattice of closed subsets of any topological space is isomorphic to that of a T0-topological space. This result is extended to lattices of closed subsets with respect to arbitrary closure operator on a set. Also, we establish a one-to-one correspondence between closure operators which are both algebraic and topological on a given set X and pre-orders on X and prove that this correspondence induces a one-to-one correspondence between topological algebraic T0-closure operators on X and partial orders on X.

Keywords and phrases

Closure operator Moore class algebraic lattice T0-closure operator pre-order 

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References

  1. 1.
    G. Birkhoff, Lattice Theory, Am. Math. Soc. Colloq. Publ. (AMS, Providence, USA, 1967), Vol. 25.Google Scholar
  2. 2.
    G. Gratzer, General Lattice Theory (Academic, New York, San Fransisco, 1978).CrossRefzbMATHGoogle Scholar
  3. 3.
    G. F. Simmons, Introduction to Topology and Modern Analysis (McGraw-Hill, New York, 1963).zbMATHGoogle Scholar
  4. 4.
    S. Burris and H. P. Sankappanavar, A Course in Universal Algebra (Springer, New York, 1980).zbMATHGoogle Scholar
  5. 5.
    U. M. Swamy, G. C. Rao, R. S. Rao, and K. R. Rao, “The lattice of closed subsets of a topological space,” South East Asian Bull. Math. 21, 91–94 (1997).MathSciNetzbMATHGoogle Scholar
  6. 6.
    U. M. Swamy and R. S. Rao, “Algebraic Topological Closure Operators,” South East Asian Bull. Math. 26, 669–678 (2002).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    B. Venkateswarlu, R. Vasu Babu, and Getnet Alemu, “Morphisms on Closure spaces andMoore spaces,” Int. J. Pure Appl. Math. 91, 197–207 (2014).CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Department of MathematicsGITAM UniversityBenguluru RuralIndia
  2. 2.Department of MathematicsAndhra UniversityVisakhapatnamIndia

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