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On µsp-Continuous Maps in Topological Spaces

Year 2019, Issue: 29, 111 - 119, 30.12.2019

Selvaraj Ganesan Rajamanickam Selva Vinayagam Balakrishnan Sarathkumar

Abstract

In this paper, we introduce a new class of continuous maps called µsp-continuous maps and study their properties in topological spaces.

Keywords

Topological space µsp-closed set µsp-continuous map µsp-irresolute map

References

  • M. E. Abd El-Monsef, S. N. El-Deeb, R. A. Mahmoud, β-Open Sets and β-Continuous Mapping, Bulletin of the Faculty of Science Assiut University 12 (1983) 77-90.
  • R. Devi, K. Balachandran, H. Maki, Semi-Generalized Homeomorphisms and Generalized Semi-Homeomorphisms in Topological Spaces, Indian Journal of Pure and Applied Mathematics 26 (1995) 271-284.
  • R. Devi, K. Balachandran, H. Maki, Generalized α-Closed Maps and α-Generalized Closed Maps, Indian Journal of Pure and Applied Mathematics 29 (1998) 37-49.
  • J. Dontchev, M. Ganster, On δ-Generalized Closed Sets and T3/4-Spaces, Memoirs of the Faculty of Science Kochi University Series A Mathematics 17 (1996) 15-31.
  • A. S. Mashhour, M. E. Abd El-Monsef, S. N. El-Deeb, On Precontinuous and Weak Precontinuous Mappings, Proceedings of the Mathematical and Physical Society of Egypt 53 (1982) 47-53.
  • M. Sheik John, A Study on Generalizations of Closed Sets and Continuous Maps in Topological and Bitopological Spaces, PhD dissertation, Bharathiar University (2002) Coimbatore, India.
  • M. K. R. S. Veera Kumar, ĝ-Closed Sets in Topological Spaces, Bulletin of The Allahabad Mathematical Society 18 (2003) 99-112.
  • K. Balachandran. P. Sundaram, H. Maki, On Generalized Continuous Maps in Topological Spaces, Memoirs of the Faculty of Science Kochi University Series A Mathematics 12 (1991) 5-13.
  • S. Ganesan, R. Selva Vinayagam, B. Sarathkumar, On µsp-Closed Sets in Topological Spaces, Proceedings International Conference on Emerging Trends and Challenges in Mathematics, December 28, NPR Arts and Science College, Tamil Nadu, (2018) 82-97.
  • O. Njastad, On Some Classes of Nearly Open Sets, Pacific Journal of Mathematics 15 (1965) 961-970.
  • N. Levine, Semi-Open Sets and Semi-Continuity in Topological Spaces, The American Mathematical Monthly 70 (1963) 36-41.
  • D. Andrijevic, Semi-Preopen Sets, Matematički Vesnik 38 (1986) 24-32.
  • S. G. Crossley, S. K. Hildebrand, Semi-Closure, Texas Journal of Science 22 (1971) 99-112.
  • T. Noiri, H. Maki, J. Umehara, Generalized Preclosed Functions, Memoirs of the Faculty of Science Kochi University Series A Mathematics 19 (1998) 13-20.
  • N. Levine, Generalized Closed Sets in Topology, Rendiconti del Circolo Matematico di Palermo 19(2) (1970) 89-96.
  • S. P. Arya, T. M. Nour, Characterization of S-Normal Spaces, Indian Journal of Pure and Applied Mathematics 21(8) (1990) 717-719.
  • H. Maki, R. Devi, K. Balachandran, Associated Topologies of Generalized α-Closed Sets and α-Generalized Closed Sets, Memoirs of the Faculty of Science Kochi University Series A Mathematics 15 (1994) 51-63.
  • H. Maki, R. Devi, K. Balachandran, Generalized α-Closed Sets in Topology, Bulletin of Fukuoka University of Education Part III 42 (1993) 13-21.
  • M. K. R. S. Veera Kumar, g#-Closed Sets in Topological Spaces, Kochi Journal of Mathematics 24 (2003) 1-13.
  • J. Dontchev, On Generalizing Semi-Preopen Sets, Memoirs of the Faculty of Science Kochi University Series A Mathematics 16 (1995) 35-48.
  • M. K. R. S. Veera Kumar, Between g*-Closed Sets in Topological Spaces, Antarctica Journal of Mathematics 3(1) (2006) 43-65.
  • M. K. R. S. Veera Kumar, #g-Semi-Closed Sets in Topological Spaces, Antarctica Journal of Mathematics 2(2) (2005) 201-222.
  • M. K. R. S. Veera Kumar, Between Closed Sets and g-Closed Sets, Memoirs of the Faculty of Science Kochi University 21 (2000) 1-19.
  • M. K. R. S. Veera Kumar, µ-Closed Sets in Topological Spaces, Antarctica Journal of Mathematics 2(1) (2005) 1-18.
  • M. K. R. S. Veera Kumar, µp-Closed Sets in Topological Spaces, Antarctica Journal of Mathematics 2(1) (2005) 31-52.
  • M. K. R. S. Veera Kumar, µs-Closed Sets in Topological Spaces, Antarctica Journal of Mathematics 2(1) (2005) 91-109.
  • A. S. Mashhour, I. A. Hasanein, S. N. El-Deeb, α-Continuous and α-Open Mappings, Acta Mathematica Hungarica 41(3-4) (1983) 213-218.
  • R. Devi, K. Balachandran, H. Maki, On Generalized α-Continuous Maps and α-Generalized Continuous Maps, Far East Journal of Mathematical Sciences Special Volume part I (1997) 1-15.

Year 2019, Issue: 29, 111 - 119, 30.12.2019

Selvaraj Ganesan Rajamanickam Selva Vinayagam Balakrishnan Sarathkumar

Abstract

References

  • M. E. Abd El-Monsef, S. N. El-Deeb, R. A. Mahmoud, β-Open Sets and β-Continuous Mapping, Bulletin of the Faculty of Science Assiut University 12 (1983) 77-90.
  • R. Devi, K. Balachandran, H. Maki, Semi-Generalized Homeomorphisms and Generalized Semi-Homeomorphisms in Topological Spaces, Indian Journal of Pure and Applied Mathematics 26 (1995) 271-284.
  • R. Devi, K. Balachandran, H. Maki, Generalized α-Closed Maps and α-Generalized Closed Maps, Indian Journal of Pure and Applied Mathematics 29 (1998) 37-49.
  • J. Dontchev, M. Ganster, On δ-Generalized Closed Sets and T3/4-Spaces, Memoirs of the Faculty of Science Kochi University Series A Mathematics 17 (1996) 15-31.
  • A. S. Mashhour, M. E. Abd El-Monsef, S. N. El-Deeb, On Precontinuous and Weak Precontinuous Mappings, Proceedings of the Mathematical and Physical Society of Egypt 53 (1982) 47-53.
  • M. Sheik John, A Study on Generalizations of Closed Sets and Continuous Maps in Topological and Bitopological Spaces, PhD dissertation, Bharathiar University (2002) Coimbatore, India.
  • M. K. R. S. Veera Kumar, ĝ-Closed Sets in Topological Spaces, Bulletin of The Allahabad Mathematical Society 18 (2003) 99-112.
  • K. Balachandran. P. Sundaram, H. Maki, On Generalized Continuous Maps in Topological Spaces, Memoirs of the Faculty of Science Kochi University Series A Mathematics 12 (1991) 5-13.
  • S. Ganesan, R. Selva Vinayagam, B. Sarathkumar, On µsp-Closed Sets in Topological Spaces, Proceedings International Conference on Emerging Trends and Challenges in Mathematics, December 28, NPR Arts and Science College, Tamil Nadu, (2018) 82-97.
  • O. Njastad, On Some Classes of Nearly Open Sets, Pacific Journal of Mathematics 15 (1965) 961-970.
  • N. Levine, Semi-Open Sets and Semi-Continuity in Topological Spaces, The American Mathematical Monthly 70 (1963) 36-41.
  • D. Andrijevic, Semi-Preopen Sets, Matematički Vesnik 38 (1986) 24-32.
  • S. G. Crossley, S. K. Hildebrand, Semi-Closure, Texas Journal of Science 22 (1971) 99-112.
  • T. Noiri, H. Maki, J. Umehara, Generalized Preclosed Functions, Memoirs of the Faculty of Science Kochi University Series A Mathematics 19 (1998) 13-20.
  • N. Levine, Generalized Closed Sets in Topology, Rendiconti del Circolo Matematico di Palermo 19(2) (1970) 89-96.
  • S. P. Arya, T. M. Nour, Characterization of S-Normal Spaces, Indian Journal of Pure and Applied Mathematics 21(8) (1990) 717-719.
  • H. Maki, R. Devi, K. Balachandran, Associated Topologies of Generalized α-Closed Sets and α-Generalized Closed Sets, Memoirs of the Faculty of Science Kochi University Series A Mathematics 15 (1994) 51-63.
  • H. Maki, R. Devi, K. Balachandran, Generalized α-Closed Sets in Topology, Bulletin of Fukuoka University of Education Part III 42 (1993) 13-21.
  • M. K. R. S. Veera Kumar, g#-Closed Sets in Topological Spaces, Kochi Journal of Mathematics 24 (2003) 1-13.
  • J. Dontchev, On Generalizing Semi-Preopen Sets, Memoirs of the Faculty of Science Kochi University Series A Mathematics 16 (1995) 35-48.
  • M. K. R. S. Veera Kumar, Between g*-Closed Sets in Topological Spaces, Antarctica Journal of Mathematics 3(1) (2006) 43-65.
  • M. K. R. S. Veera Kumar, #g-Semi-Closed Sets in Topological Spaces, Antarctica Journal of Mathematics 2(2) (2005) 201-222.
  • M. K. R. S. Veera Kumar, Between Closed Sets and g-Closed Sets, Memoirs of the Faculty of Science Kochi University 21 (2000) 1-19.
  • M. K. R. S. Veera Kumar, µ-Closed Sets in Topological Spaces, Antarctica Journal of Mathematics 2(1) (2005) 1-18.
  • M. K. R. S. Veera Kumar, µp-Closed Sets in Topological Spaces, Antarctica Journal of Mathematics 2(1) (2005) 31-52.
  • M. K. R. S. Veera Kumar, µs-Closed Sets in Topological Spaces, Antarctica Journal of Mathematics 2(1) (2005) 91-109.
  • A. S. Mashhour, I. A. Hasanein, S. N. El-Deeb, α-Continuous and α-Open Mappings, Acta Mathematica Hungarica 41(3-4) (1983) 213-218.
  • R. Devi, K. Balachandran, H. Maki, On Generalized α-Continuous Maps and α-Generalized Continuous Maps, Far East Journal of Mathematical Sciences Special Volume part I (1997) 1-15.
There are 28 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Selvaraj Ganesan This is me

Rajamanickam Selva Vinayagam This is me

Balakrishnan Sarathkumar This is me

Publication Date December 30, 2019
Submission Date January 20, 2019
Published in Issue Year 2019 Issue: 29

Cite

APA Ganesan, S., Vinayagam, R. S., & Sarathkumar, B. (2019). On µsp-Continuous Maps in Topological Spaces. Journal of New Theory(29), 111-119.
AMA Ganesan S, Vinayagam RS, Sarathkumar B. On µsp-Continuous Maps in Topological Spaces. JNT. December 2019;(29):111-119.
Chicago Ganesan, Selvaraj, Rajamanickam Selva Vinayagam, and Balakrishnan Sarathkumar. “On sp-Continuous Maps in Topological Spaces”. Journal of New Theory, no. 29 (December 2019): 111-19.
EndNote Ganesan S, Vinayagam RS, Sarathkumar B (December 1, 2019) On µsp-Continuous Maps in Topological Spaces. Journal of New Theory 29 111–119.
IEEE S. Ganesan, R. S. Vinayagam, and B. Sarathkumar, “On µsp-Continuous Maps in Topological Spaces”, JNT, no. 29, pp. 111–119, December 2019.
ISNAD Ganesan, Selvaraj et al. “On sp-Continuous Maps in Topological Spaces”. Journal of New Theory 29 (December 2019), 111-119.
JAMA Ganesan S, Vinayagam RS, Sarathkumar B. On µsp-Continuous Maps in Topological Spaces. JNT. 2019;:111–119.
MLA Ganesan, Selvaraj et al. “On sp-Continuous Maps in Topological Spaces”. Journal of New Theory, no. 29, 2019, pp. 111-9.
Vancouver Ganesan S, Vinayagam RS, Sarathkumar B. On µsp-Continuous Maps in Topological Spaces. JNT. 2019(29):111-9.
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