New Sets on Local functions of Different Perfect sets in Micro Ideal Topological Spaces

Authors

  • Ms. G. Gincy  Research Scholar, Department of Mathematics, L.R.G. Government Arts College for Women, Tirupur, Tamil Nadu, India
  • Dr. C. Janaki  Assistant Professor, Department of Mathematics, L.R.G. Government Arts College for Women, Tirupur, Tamil Nadu, India

DOI:

https://doi.org/10.32628/IJSRSET2310371

Keywords:

Micro topological spaces, Micro ideal topological spaces, , Perfect sets.

Abstract

A perfect set is one of the characterizations for compatible ideals in an ideal topological space. In this paper, we introduce and in a brand new ideal space called Micro ideal topological spaces, which give the local functions of certain perfect sets in the space and study their properties. Also we obtain a generalized topology via ideals using which is finer than micro topology and also .

References

  1. F. G. Arenas, J.Dontchev and M.L.Puertas, “Idealization of some weak separation axioms,” Acta Mathematica Hungarica,vol.89,no.1-2, 47-53,2000.
  2. G.Aslim, A.Caksu Guler and T.Noiri, “On decomposition of continuity and some weaker forms of continuity via idealization”, Acta Mathematica Hungarica, vol 109, no. 3,183-190, 2005.
  3. S. Chandrasekar, “On Micro Topological Spaces”, Journal of New Theory, No. 26, 23-31, 2019.
  4. J.Dontchev, M.Ganster and D.Rose, “Ideal Resolvability”, Topology and its applications, vol 93, no. 1, 1-16, 1999.
  5. E. Hayashi, Topologies defined by local properties, Math. Ann. 156, 205–215, 1964.
  6. T.R.Hamlett and D.Jankovic, “Ideals in general topology”, General Topology and Application, 115-125, 1988.
  7. T.R.Hamlett and D.Jankovic, “Ideals in topological spaces and the set operatory”, Bullettino della Unione Matematica Italiana, vol. 7, 863-874, 1990.
  8. D.Janovic and T.R.Hamlett, “Compatible extensions of ideals”, Bullettino della Unione Matematica Italiana, vol. 7, no. 6, 453-465, 1992.
  9. D.Janovic and T.R.Hamlett, “New topologies from old via ideals”,The American Mathematical Monthly, vol 97, 295-310, 1990.
  10. M. Lellis Thivagar and C. Richard, On Nano forms of weakly open sets, International Journal of Mathematics and statistics invention,  Vol 1(1), 31-37, 2013.
  11. M. Lellis Thivagar and V. Sutha Devi, “New sort of operators in Nano ideal topology”,  Vol 28(1)A, 51-64, 2016.
  12. R.Manoharan and P.Thangavelu, “Some new sets and topologies in Ideal topological spaces”, Chinese journal of mathematics, 1-6, 2013.

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Published

2023-06-30

Issue

Section

Research Articles

How to Cite

[1]
Ms. G. Gincy, Dr. C. Janaki "New Sets on Local functions of Different Perfect sets in Micro Ideal Topological Spaces" International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 10, Issue 3, pp.190-196, May-June-2023. Available at doi : https://doi.org/10.32628/IJSRSET2310371