Parimala MANI

A Note on Urysohn's Lemma under mIg-Normal Spaces and mIg-Regular Spaces in Ideal Minimal Spaces

This research article is concerned with the introduction of a new notion of normal spaces and regular spaces, namely mIg-normal spaces and mIg-regular spaces. We established their signicant properties in ideal minimal spaces. Some equivalent conditions on mIg-normal spaces and mIg-regular spaces are proved. Urysohn's Lemma on mIg-normal spaces is also established.

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[1] K. Kuratowski, Topology, Vol. I, Academic Press, Newyork, 1996.
[2] R. Vaidyanathaswamy, The Localization Theory in Set Topology, Proceedings of the Indian Academy of Sciences-Section A 20 (1944) 51{61.
[3] H. Maki, J. Umehara, T. Noiri. Every Topological Spaces in pre T(1=2), Memoirs of the Faculty of Science Kochi University Series A Mathematics 17 (1996) 33{42.
[4] N. Levine, Generalised Closed Sets in Topology, Rendiconti del Circolo Matematico di Palermo 2(19) (1970) 89{96.
[5] W. K. Min, m-Open Sets and m-Continuous Functions, Communications of the Korean Mathematical Society 25(2) (2010) 251{256.
[6] T. Noiri, V. Popa, A Uni ed Theory of Closed Functions, Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie 49(97) (2006) 371{382.
[7] V. Popa, T. Noiri, On Weakly (;m)-Continuous Functions, Rendiconti Del Circolo Matematico Di Palermo, Serie II, TomoLi (2002) 295{310.
[8] V. Popa, T. Noiri, On m-Continuous Functions, Annals of Dunarea de Jos University of Galati. Fascicle II, Mathematics, Physics, Theoretical Mechanics 18(23) (2000) 31{41.
[9] M. Singha, S. D. Sarkar, Towards Urysohn's Lemma in Minimal Structures, International Journal of Pure and Applied Mathematics 85(2) (2013) 255{263.
[10] O. B. Ozbakr, E. D. Yldrm, On Some Closed Sets in Ideal Minimal Spaces, Acta Mathematica Hungarica 125(3) (2009) 227{235.
[11] H. Li, Z. Li, On mIg-Normal Spaces, Journal of Applied Functional Analysis 7(1-2) (2012) 185{ 193.
[12] D. Arivuoli, M. Parimala, On Generalised Closed Sets in Ideal Minimal Spaces, Asia Life Sciences 1 (2017) 85{92.
[13] M. Parimala, D. Arivuoli, R.Perumal, On Some Locally Closed Sets in Ideal Minimal Spaces, International Journal of Pure and Applied Mathematics, 113(12) (2017) 230{238.
[14] M. Parimala, D. Arivuoli, S. Krithika, Separation Axioms in Ideal Minimal Spaces, International Journal of Recent Technology and Engineering 7(4S2) (2018) 373{375.
[15] T. Noiri, V. Popa, On m-D-Separation Axioms, istanbul University Science Faculty the Journal of Mathematics, Physics and Astronomy 61-62 (2002-2003) 15{28.
[16] M. Parimala, D. Arivuoli, Submaximality under mI g-Closed Sets in Ideal Minimal Spaces, Asia Mathematika 3(2) (2019) 63{71.