Minimal Feebly Semiseparated $\check{C}$ech-closure Spaces

Yogesh Prasad1 and T. P. Johnson1


1Department of Mathematics, Cochin University of Science \& Technology, Cochin, Kerala, India.

Abstract: In this paper we introduce the concept of Minimal feebly semiseparated, semiseparated $\check{C}$ech closure spaces. The relation between the underlying topological spaces of the minimal feebly semiseparated closure spaces are also investigated. Properties of sets (open, closed) in minimal feebly semiseparated closure spaces are investigated. A weak characterisation theorem for finite minimal feebly semisepaprted closure space is obtained.
Keywords: $\check{C}$ech closure spaces, Feebly semiseperated $\check{C}$ech closure spaces, Minimal feebly semiseparated $\check{C}$ech closure spaces.


Cite this article as: Yogesh Prasad and T. P. Johnson, Minimal Feebly Semiseparated $\check{C}$ech-closure Spaces, Int. J. Math. And Appl., vol. 9, no. 4, 2021, pp. 45-51.

References
  1. M. P. Berri, \textit{Minimal topological spaces}, Trans. Amer. Math. Soc., 108(1963), 97-105.
  2. D. E. Cameron, \textit{A survey of maximal topological spaces}, Topology Proc., 2(1977), 11-60.
  3. D. E. Cameron, \textit{Maximal and minimal topologies}, Trans. Amer. Math.Soc., 160(1971), 229-248.
  4. E. $\check{C}$ech, \textit{Topological Spaces}, Wiley, London, (1966).
  5. P. H. Doyle, \textit{On finite $T_{0}$ spaces}, General topology and its relationship to modern analysis and algebra, {\bf II}, $2^{nd}$ Prague Top. Symp., (1966), 115-117.
  6. E. Hewitt, \textit{A problem of set theoretic topology}, Duke Math. J., 10(1943), 309-333.
  7. T. Kavitha, \textit{Simple expansions in the lattice of Cech closure operators}, Palestine Journal of Mathematics, 8(1)(2019), 1-7.
  8. R. E. Larson, \textit{On the lattice of topologies}, Thesis for Ph.D. Degree, University of Colorado, (1970).
  9. A. S. Mashhour and M. H. Ghanim, \textit{On Closure Spaces}, Indian J. Pure Appl. Math., 14(6)(1983), 680-691.
  10. Ki-Hyun Pahk, \textit{Note on the characterisation of minimal $T_{0}$ and $T_{D}$ spaces}, Kyungpook Mathematical Journal, 8(1)(1968), 5-10.
  11. A. S. Parhomenko, \textit{Uber eineindeutige steige Abbildungen}, Mat. Sb., 5(47)(1939), 197-210.
  12. D. N. Roth and J. W. Carlson, \textit{Cech closure spaces}, Kyungpook Mathematical Journal, 20(1980), 11-30.
  13. N. Smythe and C. A. Wilkins, \textit{Minimal Hausdorff and maximal compact spaces}, J. Austral. Math. Soc., 3(1963), 167-171.
  14. T. A. Sunitha, \textit{A study of $\check{C}$ech closure spaces}, Thesis for Ph.D. Degree, Cochin University of Science and Technology, (1994).
  15. W. J. Thron, \textit{What results are valid in closure spaces}, Blacksburg Topology Conference Spring, (1981).
  16. Yogesh Prasad and T. P. Johnson, \textit{A note on maximal and minimal $\check{C}$ech closure spaces }, (communicated).

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