Pairwise Paracompactness

Authors

  • Pallavi S. Mirajakar Department of Mathematics (P. C. Jabin Science College, Hubbali,Karnatak, India)
  • P.G. Patil Department of Mathematics Karnatak University, Dharwad-580003, India

DOI:

https://doi.org/10.23755/rm.v38i0.495

Keywords:

(τi, τj)-g∗ωα-closed sets, τj)-g∗ωα-open sets, τj)-g∗ωα-continuous and (τi, τj)-g∗ωα-irresolute maps, τj)-g∗ωα-paracompact spaces.

Abstract

The purpose of this paper is to introduce and study a new paracompactness in bitopological spaces using (τi, τj)-g∗ωα-closed sets. Further, the properties of (τi, τj)-g∗ωα-closed sets, (τi, τj)-g∗ωα- continuous functions and (τi, τj)-g∗ωα-irresolute maps and (τi, τj)- g∗ωα-paracompact spaces are discussed in bitopological spaces.

 

Author Biography

  • P.G. Patil, Department of Mathematics Karnatak University, Dharwad-580003, India

    P.G.Patil

    Professor of Mathematics

    Karnatak University, Dharwad-580003, India

References

. I. Arockiarani, Studies on Generalizations of Generalized Closed Sets and Maps in Topological Spaces, Ph.D., Thesis, Bharathiar Univ., Coimbatore, (1997).

S. S. Benchalli, P. G. Patil and T. D. Rayanagaudar, !-Closed Sets is Topological Spaces, The Global. Jl. Appl. Math. and Math. Sci., 2, (2009), 53-63.

R. Devi, K. Balachandran and H. Maki, Semi-Generalized Closed Maps and Generalized Semi-Closed Maps, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 14(1993), 41-54.

O. A. El-Tntawy and H. M. Abu-Donia, Generalized Separation Axioms in Bitopological Spaces, The Arabian Jl. for Sci. and Engg., Vol. 30(1) A, (2005),117-129.

T. Fukutake, On Generalized Closed Sets in Bitopological Spaces, Bull. Fukuoka Univ. Ed. Part III, 35 (1986), 19-28.

T. Fukutake, P. Sundaram and M. Shaik John, On omega-Closed Sets, omega -Open Sets and omega -Continuity in Bitopological Spaces, Bull. Fukuoka Univ. Edn., 35, Part III, 51 (2002), 1-9.

Y. Gnanambal, Studies on Generalized Pre-Regular Closed Sets and Generalization of Locally Closed Sets, Ph.D Thesis, Bharathiar University, Coimbatore,(1998).

J. C. Kelly, Bitopological Spaces, Proc. London Math. Society, 13 (1963),71-89.

F. H. Khedr and H. S. Al-saadi, On Pairwise Semi-Generalized Closed Sets,(submitted).

H. Maki, P. Sundaram and K. Balachandran, On Generalized Continuous Maps and Pasting Lemma in Bitopological Spaces, Bull. Fukuoka Univ. Ed. Part III, 40 (1991), 23-31.

P. G. Patil, omega alpha-Closed Sets in Bitopological Spaces, International Jl. of Advances in Management, Technology and Engineering Sciences, Vol.II, 3(IV)(2012), 111-114.

P. G. Patil, S. S. Benchalli and P. S. Mirajakar, Generalized Star omega alpha-Closed Sets in Topological Spaces, Jl. of New Results in Science, Vol 9, (2015), 37-45.

P. G. Patil, S. S. Benchalli, P. S. Mirajakar and S. Jafari, New Class of Paracompact Spaces in Topological Spaces (Communicated).

M. Sheik John and P. Sundaram, g*-Closed Sets in Bitopological Spaces, IndianJl. Pure Appl. Math., 35(1)(2004), 71-80.

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Published

2020-06-30

Issue

Vol. 38 (2020)

Section

Volume 38-2020

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