Strongly k-spaces

Document Type : Research Paper


1 Department of Mathematics‎, ‎Faculty of Arts and Sciences‎, ‎Sakarya University‎, ‎Sakarya‎, ‎54187‎, ‎Turkey.

2 Department of Mathematics, Faculty of Arts and Sciences, Sakarya University, Sakarya, 54187 TURKEY


‎In this paper‎, ‎we introduce the notion of strongly $k-$spaces (with the weak (=finest) pre-topology generated by their strongly compact subsets)‎. ‎We characterize the strongly $k-$spaces and investigate the relationships between preclosedness‎, ‎locally strongly compactness‎, ‎pre-first countableness and being strongly $k-$space.


Main Subjects

R.F. Arens, A topology for spaces of transformations, Ann. of Math. (2) 47 (1946) 480--495.
R.H. Atia, S.N. El-Deeb and I.A. Hasanein, A note on strong compactness and S-closedness, Mat. Vesnik 6 (1982), no. 1, 23--28.
J.B.T. Ayawan and S.R. Canoy, Axioms of countability in generalized topological spaces, Int. Math. Forum 8 (2013), no. 29-32, 1523--1530.
D.E. Cohen, Spaces with weak topology, Q. J. Math. Oxford Ser. (2) 5 (1953) 77--80.
J. Dontchev, Survey on preopen sets, in: The Proceedings of the Yatsushiro Topological Conference, 1998, pp. 1--18.
M. Ganster, Some remarks on strongly compact spaces and semi-compact spaces, Bull. Malays. Math. Soc. (2) 10 (1987), no. 2, 67--70.
S. Jafari and T. Noiri, More on strongly compact spaces, Missouri J. Math. Sci. 19 (2007), no. 1, 52--61.
Y.B. Jun, S.W. Jeong, H.J. Lee and J.W. Lee, Applications of pre-open sets, Appl. Gen. Topol. 9 (2008), no. 2, 213--228.
J.L. Kelley, General Topology, D. Van Nostrand, New York, 1955.
N.E. Liden, K-spaces, their antispaces and related mappings, Pacific J. Math. 59 (1975), no. 2, 505--514.
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.
A.S. Mashhour, M.E. Abd El-Monsef, I.A. Hasanein and T. Noiri, Strongly compact spaces, Delta J. Sci. 8 (1984) 30--46.
A.S. Mashhour, I.A. Hasanein and S.N. El-Deeb, A note on semicontinuity and precontinuity, Indian J. Pure Appl. Math. 13 (1982), no. 10, 1119--1123.
M.C. McCord, Classifying spaces and infinite symmetric products, Trans. Amer. Math. Soc. 146 (1969) 273--298.
M. Mirmiran, Insertion of a -continuous function, Bull. Iranian Math. Soc. 37 (2011), no. 3, 171--181.
A.I. Nasir, Strongly C-compactness, J. Al-Nahrain Univ. 15 (2012), no. 1, 140--144.
N.L. Noble, K-spaces and some generalizations, PhD Thesis, University of Rochester, ProQuest LLC, Ann Arbor, 1967.
T.M. Nour, Pre-unique sequential spaces, Indian J. Pure Appl. Math. 32 (2001), no. 6, 797--800.
V. Popa, Characterization of H-almost continuous functions, Glas. Mat. Ser. III 22 (1987), no. 1, 157--161.
N.E. Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967) 133--152.
R.C. Steinlage, On Ascoli theorems and the product of k-spaces, Kyungpook Math. J. 12 (1972) 145--151.
D.D. Weddington, On k-spaces, Proc. Amer. Math. Soc. 22 (1969) 635--638.
S. Weingram, Bundles, realizations, and k-spaces, PhD Thesis, Princeton University, 1962.