Separation axioms of αm-contra-open maps and b-ω-open sets in generalized topological spaces

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-3935

Keywords:

Generalized topological spaces, Tαm-Super-Spaces, αmcontra-closed maps, αm-contra-open maps, αm-contra-continuous maps, αm-contra-irresolute maps and b-ω-open sets

Abstract

In this paper, we introduce Tαm-Super-Spaces, αm-contra-closed maps, αm-contra-open maps, αm-contra-continuous maps, αm-contrairresolute maps, b-ω-open sets and Continuity via b-ω-open sets and studied some of their properties

Author Biographies

Boulbaba Ghanmi, University of Gafsa.

Département de Mathématiques, Facultée des Sciences.

Rim Messaoud, University of Gafsa.

Département de Mathématiques, Facultée des Sciences

Amira Missaoui, University of Gabès.

Département de Mathématiques, Facultée des Sciences

References

D. Andrijevic, “Semi-preopen sets”, Matematički Vesnik, vol. 38, pp. 24-32, 1986.

D. Andrijevic, “On b-open sets”, Matematički Vesnik, vol. 48, pp. 59-64, 1996.

S. P. Arya and T. Nour, “Characterizations of s-normal spaces”, Indian Journal of Pure and Applied Mathematics, vol. 21, pp. 717-719, 1990.

P. Bhattacharyya and B. K. Lahiri, “Semi-generalized closed sets in topology”, Indian Journal of Mathematics, vol. 29, pp. 375-382, 1987.

E. D. Khalimsky, “Applications of connected ordered topological spaces in topology,” in Conference of Math. Departments of Povolsia, 1970.

E. Khalimsky, R. Kopperman, and P. R. Meyer, “Computer graphics and connected topologies on finite ordered sets”, Topology and its Applications, vol. 36, no. 1, pp. 1-17, 1990.

T. Y. Kong, R. Kopperman, and P. R. Meyer, “A topological approach to digital topology”, The American mathematical monthly, vol. 98, pp. 901-917, 1991.

N. Levine, “Semi-open sets and semi-continuity in topological spaces”, The American mathematical monthly, vol. 70, pp. 36-41, 1963.

N. Levine, “Generalized closed sets in topology”, Rendiconti del Circolo Matematico di Palermo, vol. 19, pp. 89-96, 1970.

A. S. Mashhour, M. E. Abd El-Moncef, and S. N. El-Deeb, “On preconlinuous and weak precontinuous mappings”, Proceedings of the Mathematical and Physical Society of Egypt, vol. 53, pp. 47-53, 1982.

M. Mathew and R. Parimelzhagan, “αm-Closed Sets in Topological Spaces”, International Journal of Mathematical analysis, vol. 8, no. 47, pp. 2325-2329, 2014.

M. Mathew and R. Parimelazhagan, “Separation Axioms of αm Open Sets”, 2016, arxiv: 1601.03514

M. Mathew, R. Parimelzhagan, and S. Jafari “αm-Continuous Maps in Topological Spaces”, International Journal of Pure and Applied Mathematics, vol. 106, no. 8, pp. 161-167, 2016.

O. Njåstad, “On some classes of nearly open sets”, Pacific Journal of Mathematics, vol. 15, no. 3, pp. 961-970, 1965.

J. Dontchev, “Contra-continuous functions and strongly S-closed spaces”, International Journal of Mathematics and Mathematical Sciences, vol. 19, pp. 303-310, 1996.

S. Al Ghour and W. Zareer, “Omega open sets in generalized topological spaces”, Journal of Nonlinear Science and Applications, vol. 9, pp. 3010-3017, 2016.

S. Al Ghour, "Certain Covering Properties Related to Paracompactness", Ph.D. thesis, University of Jordan, Amman, Jordan, 1999.

S. Al Ghour, “Some generalizations of paracompactness”, Missouri Journal of. Mathematical Sciences, vol. 18, no. 1, pp. 64-77, 2006.

S. Al Ghour, A. Al-Omari, and T. Noiri, “On homogeneity and homogeneity components in generalized topological spaces”, Filomat, vol. 27, pp. 1097-1105, 2013.

A. Al-Omari and T. Noiri, “A unified theory of contra-(µ, λ)-continuous functions in generalized topological spaces”, Acta Mathematica Hungarica, vol. 135, pp. 31-41, 2012.

A. Al-Omari and M. S. Md. Noorani, “Regular generalized ω-closed sets”, International Journal of Mathematics and Mathematical Sciences, vol. 2007, Art. ID 016292, 2007. https://doi.org/10.1155/2007/16292

A. Al-Omari and M. S. Md. Noorani, “Contra-ω-continuous and almost contra-ω-continuous”, International Journal of Mathematics and Mathematical Sciences, vol. 2007, Art. ID 040469, 2007. https://doi.org/10.1155/2007/40469

K. Al-Zoubi, “On generalized ω-closed sets”, International Journal of Mathematics and Mathematical Sciences, vol. 2005, Art. ID 153616, 2005. https://doi.org/10.1155/IJMMS.2005.2011

K. Al-Zoubi, B. Al-Nashef, “The Topology of ω-open subsets”, Al Manarah Journal, vol. 9, pp. 169-179, 2003.

C. Cao, J. Yan, W. Wang, and B. Wang, “Some generalized continuities functions on generalized topological spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 2, pp. 159-163, 2013.

C. Carpintero, N. Rajesh, E. Rosas, and S. Saranyasri, “On Slightly Omega Continuous Multifunctions”, The Punjab University journal of mathematics, vol. 46, pp. 51-57, 2014.

C. Carpintero, E. Rosas, M. Salas, J. Sanabria, and L. Vasquez, “Generalization of ω-closed sets via operators and ideals”, Sarajevo journal of mathematics, vol. 9, pp. 293-301, 2013.

Á. Császár, “Generalized topology, generalized continuity”, Acta Mathematica Hungarica, vol. 96, pp. 351-357, 2002.

Á. Császár, “γ-connected sets”, Acta Mathematica Hungarica, vol. 101, pp. 273- 279, 2003

Á. Császár, “Separation axioms for generalized topologies”, Acta Mathematica Hungarica, vol. 104, pp. 63-69, 2004.

Á. Császár, “Extremally disconnected generalized topologies”, Annales Universitatis Scientiarium Budapestinensis de Rolando Eötvös Nominatae. Sectio Mathematica, vol. 47, pp. 91-96, 2004.

Á. Császár, “Generalized open sets in generalized topologies”, Acta Mathematica Hungarica, vol. 106, pp. 53-66, 2005.

Á. Császár, “Product of generalized topologies”, Acta Mathematica Hungarica, vol. 123, pp. 127-132, 2009.

R. Engelking, General Topology. Berlin: Heldermann, 1989.

H. Z. Hdeib, “ω-closed mappings”, Revista Colombiana de Matemáticas, vol. 16, no. 1-2, pp. 65-78, 1982.

Published

2021-09-29

How to Cite

[1]
B. Ghanmi, R. Messaoud, and A. Missaoui, “Separation axioms of αm-contra-open maps and b-ω-open sets in generalized topological spaces”, Proyecciones (Antofagasta, On line), vol. 40, no. 5, pp. 1249-1266, Sep. 2021.

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