Affiliation:
1. Department of Mathematics, Faculty of Science, The Hashemite University , P.O. Box 330127 , Zarqa 13133 , Jordan
Abstract
Abstract
Sarsak [M. S. Sarsak, On some properties of generalized open sets in generalized topological spaces, Demonstr. Math. 46 (2013), no. 2, 415–427] studied some properties of generalized open sets in generalized topological spaces (GTSs); the primary purpose of this article is to investigate more properties of generalized open sets in GTSs. We mainly study the behaviours of regular closed sets, semi-open sets, regular semi-open sets, preopen sets, and
β
\beta
-open sets in GTSs analogous to their behaviours in topological spaces.
Reference26 articles.
1. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41, http://doi.org/10.1080/00029890.1963.11990039.
2. A. S. Mashhour, M. E. Abd El-Monsef, and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53 (1982), 47–53.
3. M. E. Abd El-Monsef, S. N. El-Deeb, and R. A. Mahmoud, β-open sets and β-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77–90.
4. Á. Császár, Generalized open sets in generalized topologies, Acta Math. Hungar. 106 (2005), no. 1–2, 53–66, http://doi.org/10.1007/s10474-005-0005-5.
5. M. S. Sarsak, On some properties of generalized open sets in generalized topological spaces, Demonstr. Math. 46 (2013), no. 2, 415–427, http://doi.org/10.1515/dema-2013-0453.