Research Article
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Year 2021, , 11 - 19, 30.06.2021
https://doi.org/10.53570/jnt.846524

Abstract

References

  • K. Kuratowski, Topology, Vol. I, Academic Press, Newyork, 1996.
  • R. Vaidyanathaswamy. The Localization Theory in Set Topology, Proceedings of the Indian Academy of Sciences-Section A 20 (1944) 51-61.
  • 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.
  • N. Levine, Generalised Closed Sets in Topology, Rendiconti del Circolo Matematico di Palermo 2(19) (1970) 89-96. W. K. Min, αm-Open Sets and αm-Continuous Functions, Communications of the Korean Mathematical Society 25(2) (2010) 251-256. T. Noiri, V. Popa, A Unified Theory of Closed Functions, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie 49(97) (2006) 371-382.
  • V. Popa, T. Noiri, On Weakly (τ,m)-Continuous Functions, Rendiconti Del Circolo Matematico Di Palermo, Serie II, TomoLi (2002) 295-310.
  • V. Popa, T. Noiri, On m-Continuous Functions, Annals of Dun\u area de Jos University of Galati. Fascicle II, Mathematics, Physics, Theoretical Mechanics 18(23) (2000) 31-41.
  • M. Singha, S. D. Sarkar, Towards Urysohn's Lemma in Minimal Structures, International Journal of Pure and Applied Mathematics 85(2) (2013) 255-263. O. B. Özbakır, E. D. Yıldırım, On Some Closed Sets in Ideal Minimal Spaces, Acta Mathematica Hungarica 125(3) (2009) 227-235.
  • H. Li, Z. Li, On mIg-Normal Spaces, Journal of Applied Functional Analysis 7(1-2) (2012) 185-193.
  • D. Arivuoli, M. Parimala, On α Generalised Closed Sets in Ideal Minimal Spaces, Asia Life Sciences 1 (2017) 85-92. 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.
  • M. Parimala, D. Arivuoli, S. Krithika, Separation Axioms in Ideal Minimal Spaces, International Journal of Recent Technology and Engineering 7(4S2) (2018) 373-375.
  • 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.
  • M. Parimala, D. Arivuoli, Submaximality under mIαg-Closed Sets in Ideal Minimal Spaces, Asia Mathematika 3(2) (2019) 63-71.

A Note on Urysohn’s Lemma under mIαg-Normal Spaces and mIαg-Regular Spaces in Ideal Minimal Space

Year 2021, , 11 - 19, 30.06.2021
https://doi.org/10.53570/jnt.846524

Abstract

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

References

  • K. Kuratowski, Topology, Vol. I, Academic Press, Newyork, 1996.
  • R. Vaidyanathaswamy. The Localization Theory in Set Topology, Proceedings of the Indian Academy of Sciences-Section A 20 (1944) 51-61.
  • 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.
  • N. Levine, Generalised Closed Sets in Topology, Rendiconti del Circolo Matematico di Palermo 2(19) (1970) 89-96. W. K. Min, αm-Open Sets and αm-Continuous Functions, Communications of the Korean Mathematical Society 25(2) (2010) 251-256. T. Noiri, V. Popa, A Unified Theory of Closed Functions, Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie 49(97) (2006) 371-382.
  • V. Popa, T. Noiri, On Weakly (τ,m)-Continuous Functions, Rendiconti Del Circolo Matematico Di Palermo, Serie II, TomoLi (2002) 295-310.
  • V. Popa, T. Noiri, On m-Continuous Functions, Annals of Dun\u area de Jos University of Galati. Fascicle II, Mathematics, Physics, Theoretical Mechanics 18(23) (2000) 31-41.
  • M. Singha, S. D. Sarkar, Towards Urysohn's Lemma in Minimal Structures, International Journal of Pure and Applied Mathematics 85(2) (2013) 255-263. O. B. Özbakır, E. D. Yıldırım, On Some Closed Sets in Ideal Minimal Spaces, Acta Mathematica Hungarica 125(3) (2009) 227-235.
  • H. Li, Z. Li, On mIg-Normal Spaces, Journal of Applied Functional Analysis 7(1-2) (2012) 185-193.
  • D. Arivuoli, M. Parimala, On α Generalised Closed Sets in Ideal Minimal Spaces, Asia Life Sciences 1 (2017) 85-92. 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.
  • M. Parimala, D. Arivuoli, S. Krithika, Separation Axioms in Ideal Minimal Spaces, International Journal of Recent Technology and Engineering 7(4S2) (2018) 373-375.
  • 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.
  • M. Parimala, D. Arivuoli, Submaximality under mIαg-Closed Sets in Ideal Minimal Spaces, Asia Mathematika 3(2) (2019) 63-71.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Parimala Mani 0000-0003-1390-2049

Arivuoli Dhandapanı 0000-0003-1490-2788

Publication Date June 30, 2021
Submission Date April 26, 2019
Published in Issue Year 2021

Cite

APA Mani, P., & Dhandapanı, A. (2021). A Note on Urysohn’s Lemma under mIαg-Normal Spaces and mIαg-Regular Spaces in Ideal Minimal Space. Journal of New Theory(35), 11-19. https://doi.org/10.53570/jnt.846524
AMA Mani P, Dhandapanı A. A Note on Urysohn’s Lemma under mIαg-Normal Spaces and mIαg-Regular Spaces in Ideal Minimal Space. JNT. June 2021;(35):11-19. doi:10.53570/jnt.846524
Chicago Mani, Parimala, and Arivuoli Dhandapanı. “A Note on Urysohn’s Lemma under mIαg-Normal Spaces and mIαg-Regular Spaces in Ideal Minimal Space”. Journal of New Theory, no. 35 (June 2021): 11-19. https://doi.org/10.53570/jnt.846524.
EndNote Mani P, Dhandapanı A (June 1, 2021) A Note on Urysohn’s Lemma under mIαg-Normal Spaces and mIαg-Regular Spaces in Ideal Minimal Space. Journal of New Theory 35 11–19.
IEEE P. Mani and A. Dhandapanı, “A Note on Urysohn’s Lemma under mIαg-Normal Spaces and mIαg-Regular Spaces in Ideal Minimal Space”, JNT, no. 35, pp. 11–19, June 2021, doi: 10.53570/jnt.846524.
ISNAD Mani, Parimala - Dhandapanı, Arivuoli. “A Note on Urysohn’s Lemma under mIαg-Normal Spaces and mIαg-Regular Spaces in Ideal Minimal Space”. Journal of New Theory 35 (June 2021), 11-19. https://doi.org/10.53570/jnt.846524.
JAMA Mani P, Dhandapanı A. A Note on Urysohn’s Lemma under mIαg-Normal Spaces and mIαg-Regular Spaces in Ideal Minimal Space. JNT. 2021;:11–19.
MLA Mani, Parimala and Arivuoli Dhandapanı. “A Note on Urysohn’s Lemma under mIαg-Normal Spaces and mIαg-Regular Spaces in Ideal Minimal Space”. Journal of New Theory, no. 35, 2021, pp. 11-19, doi:10.53570/jnt.846524.
Vancouver Mani P, Dhandapanı A. A Note on Urysohn’s Lemma under mIαg-Normal Spaces and mIαg-Regular Spaces in Ideal Minimal Space. JNT. 2021(35):11-9.


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