A note on pre generalized b-closed set

Downloads

DOI:

https://doi.org/10.26637/MJM0803/0081

Abstract

In this paper, we show that some results obtained in [S. Sekar and R. Brindha, On Pre Generalized B-Closed Set In Topological Spaces, Int. J. Pure Appl. Math., 111(4)(2016),577-586] are incorrect in general,by giving counter examples. Also, we illustrate that Example 3.5,Example 3.13, Example 3.15 and Example 3.17 are incorrect. Moreover, the correction form of the incorrect results of [13] is presented. Finally, we established that the concepts of b-closed sets and pgb-closed sets are same.

Keywords:

pg-closed sets, pgb-closed sets, rgb-closed sets, b-closed sets, \(g\alpha b\)-closed sets

Mathematics Subject Classification:

Mathematics
  • J.B. Toranagatti Department of Mathematics,Karnatak University’s Karnatak College, Dharwad-580001, India.
  • Pages: 1200-1202
  • Date Published: 01-07-2020
  • Vol. 8 No. 03 (2020): Malaya Journal of Matematik (MJM)

[I] D. Andrijivic, On semi pre open sets, Mat. Vesnic, 38(1986), 24-32.

D. Andrijivic, On b-open sets, Mat. Vesnic, 48(1996), 59-64.

M.E. Abd. El-Monsef, S.N. El-Deeb and R.A. Mahmoud, $beta$-open sets and $beta$-continuous mappings, Bull. Fac. Sci. Assiut Univ., 12(1983), 77-90.

A.A. El-Atik, H.M. Abu Donia, A.S. Salama, On bconnectedness and b-disconnectedness and their applications, J. Egyptian Math. Soc., 21(2013), 63-67.

J. Cao, M. Ganster, I. Reilly and M. Steiner, $delta$-closure, $theta$-closure and generalized closed sets, Applied General Topology, Universidad Politecnica de Valencia, 6(2005), 79-86.

D. Jankovic and I.L. Reilly, On semi-separation properties, Indian J. Pure Appl. Math., 16(1985), 957-964.

N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.

${ }^{[8]}$ N. Levine, Generalized closed sets in topology, Rent. Circ. Mat. Palermo, 19(1970), 89-96.

H. Maki, J. Umehara, and T. Noiri, Every topological space is pre-T $frac{1}{2}$, Mem. Fac. Sci. Kochi Univ. Math., 17(1996), 33-42.

K. Mariappa and S. Sekar, On regular generalized bclosed sets, Int. J. Math. Anal., 7(2013), 613-624.

A. S. Mashhour, M. E. Abd El-Monsef, and S. N. ELDeeb,On pre-continuous and weak pre continuous mappings, Proc. Math and Phys.Soc. Egypt, (53)(1982), 4753.

O.Njastad, On some classes of nearly open sets, Pacific. J. Math., (15)(1965), 961-970.

S. Sekar and R. Brindha, On pre generalized b-closed set in topological spaces, Int. J. Pure Appl. Math., 111(2016), $577-586$.

S. Sekar and R. Brindha, Almost contra pre generalized b-continuous functions in topological spaces, Malaya J.Mat., 5(2017), 194-201.

L. Vinayagamoorthi and N. Nagaveni, On generalized $alpha$ bclosed set, Proceeding ICMD-Allahabad, Pusbha Publication $(1),(2011), 1-10$.

  • NA

Metrics

Metrics Loading ...

Published

01-07-2020

How to Cite

J.B. Toranagatti. “A Note on Pre Generalized B-Closed Set”. Malaya Journal of Matematik, vol. 8, no. 03, July 2020, pp. 1200-2, doi:10.26637/MJM0803/0081.