Applications of pre-open sets
Keywords:Pre-limit point, Pre-derived set, Pre-interior, Pre-closure, Pre-interior points, Pre-border, Pre-frontier, Pre-exterior
Using the concept of pre-open set, we introduce and study topological properties of pre-limit points, pre-derived sets, preinterior and pre-closure of a set, pre-interior points, pre-border, prefrontier and pre-exterior. The relations between pre-derived set (resp. pre-limit point, pre-interior (point), pre-border, pre-frontier, and preexterior) and α-derived set (resp. α-limit point, α-interior (point), α-border,
α-frontier, and α-exterior) are investigated.
D. Andrijevic, Some properties of the topology of α-sets, Mat. Vesnik 36 (1984), 1–10.
M. Caldas, A note on some applications of α-sets, Int. J. Math. Math. Sci. 2003, no. 2 (2003), 125–130.
M. Caldas and J. Dontchev, On spaces with hereditarily compact α-topologies, Acta Math. Hung. 82 (1999), 121–129.
S. Jafari and T. Noiri, Contra-α-continuous functions between topological spaces, Iranian Int. J. Sci. 2, no. 2 (2001), 153–167.
S. Jafari and T. Noiri, Some remarks on weak α-continuity, Far East J. Math. Sci. 6, no. 4 (1998), 619–625.
S. N. Maheshwari and S. S. Thakur, On α-irresolute mappings, Tamkang J. Math. 11 (1980), 209–214.
S. N. Maheshwari and S. S. Thakur, On α-compact spaces, Bull. Inst. Math. Acad. Sinica 13 (1985), 341–347.
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.
H. Maki, R. Devi and K. Balachandran, Generalized α-closed sets in topology, Bull. Fukuoka Univ. Ed. Part III 42 (1993), 13–21.
H. Maki and T. Noiri, The pasting lemma for α-continuous maps, Glas. Mat. 23(43) (1988), 357–363.
A. S. Mashhour, I. A. Hasanein and S. N. El-Deeb, A note on semi-continuity and precontinuity, Indian J. Pure Appl. Math. 13, no. 10 (1982), 1119–1123.
A. S. Mashhour, I. A. Hasanein and S. N. El-Deeb, α-continuous and α-open mappings, Acta Math. Hungar. 41, no. 3-4 (1983), 213–218.
N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41.
O. Nj°astad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961–970.
I. L. Reilly and M. K. Vamanamurthy, On α-sets in topological spaces, Tamkang J. Math. 16 (1985), 7–11.
J. Tong, On decomposition of continuity in topological spaces, Acta Math. Hungar. 54, no. 1-2 (1989), 51–55.
How to Cite
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.