λ- semi compact spaces and λ- strongly compact spaces

Document Type : Original Paper

Authors

1 Department of Mathematics, Faculty of Mathematics and Mathematical Sciences, Shahid Chamran University of Ahvaz, ,Ahvaz, Iran

2 Department of Mathematics, Faculty of Mathematical Sciences and computer, Shahid Chamran University of Ahvaz,, Ahvaz, Iran

Abstract

For an infinite cardinal number λ , λ- semi compact spaces and λ-strongly compact spaces which are generalizations of semi-compact spaces and strongly compact spaces are introduced and studied. It is shown that for every infinite cardinal number λ , there exist non-discrete λ- semi compact spaces and non-discrete λ- strongly compact spaces. Basic properties of such spaces are investigated.

Keywords

Main Subjects


[1] S. G. Crossley and S. K. Hildebrand, Semi-closure, Texas J. Sci. 22 (1971) 99-112.
[2] S. G. Crossley and S. K. Hildebrand, Semi-topological properties, Fund. Math.74 (1972) 233-254.
[3] M. C. Cueva and J. Dontchev, On spaces with hereditarily compact -topologies, Acta Math. Hungar. 82(1-2) (1999) 121-129.
[4] P. Das, Note on some applications of semi-open sets, Prog. Math. 7 (1973) 33-44.
[5] J. Dontchev, M. Ganster and T. Noiri, On p-closed spaces, Int. J. Math. And Math. Sci. 24(3) (2000) 203-212.
[6] C. Dorsett, Semi-regular spaces, Soochow J. Math. 8 (1982) 45-53.
[7] C. Dorsett, Semi-compactness, Semi-separation axioms and product spaces, Bull. Malaysian Math. Soc. 4(1) (1981) 21-28.
[8] R. Engelking, General Topology, Heldermann verlag, Berlin, 1989.
[9] M. Ganster, On covering properties and generalized open sets in topological spaces, Math. Chronicle, 19 (1990) 27-33.
[10] M. Ganster, Some remarks on strongly compact spaces and semi compact spaces, Bull. Malaysian Math. Soc. 10 (1987) 67 81.
[11] M. Ganster, Preopen sets and resolvable spaces, Kyungpook Math. J. 27(2) (1987) 135-143.
[12] H. Z. Hdeib and M. S. Sarsak, On strongly lindelof spaces, Q & A in General Topology, 18 (2000) 289-298.
[13] Y. B Jun, S. W. Jeong, H. J. Lee and J. W. Lee, Applications of pre-open sets, Appl. Gen. Topol. 9(2) (2008) 213-228.
[14] A. Kar and P. Bhattacharyya, Some weak separation axioms, Bull. Calcutta Math. Soc. 82 (1990) 415-422.
[15] O. A. S. Karamzadeh, M. Namdari, and M. A. Siavoshi, A note on -compact spaces, Math. Slovaca, 63(6) (2013) 1371-1380.
[16] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. 70 (1963) 36-41.
[17] S. N. Maheshwari and R. Prasad, Some new separation axioms, Ann. Soc. Sci. Bruxelles, 89 (1975) 395-402.
[18] 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.
[19] A. S. Mashhour, M. E. Abd El-Monsef, I. A. Hasanein and T. Noiri, Strongly compact spaces, Delta J. Sci. 8 (1984) 30-46.
[20] A. S. Mashhour, M. E. Abd El-Monsef and I. A. Hasanein, On pretopological spaces, Bull. Math. Soc. Sci. Math. R. S. Roumanie, 76(1) (1984)39-45.
[21] A. S. Mashhour, I. A. Hasanein and S. N. El-Deeb, A note on semicontinuity and precontinuity, Indian J. Pure Appl. Math. 13(10) (1982) 1119-1123.
[22] M. Namdari, M. A. Siavoshi, A generalization of compact spaces, Jp J. Geom. Topol. 11(3) (2011) 259-270.
[23] O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15(3) (1965) 961-970.
[24] Z. Piotrowski, A survey of results concerning generalized continuity in topological spaces, Acta Math. Univ. Comenian. 53 (1987) 91-110.
[25] I. L. Reilly and M. K. vamanamurthy, On -continuity in topological spaces, Acta Math. Hungar. 45 (1985) 27-32.
[26] M. S. Sarsak, On semi-compact sets and associated properties, Int. J. Math. and Math. Sci. (2009) 1-8.
[27] G. Vigilino, Seminormal and C-compact spaces, Duke J. Math. 38 (1971) 57-61.