ON δgs-CLOSED SETS AND ALMOST WEAKLY HAUSDORFF SPACES

• Journal title : Honam Mathematical Journal
• Volume 29, Issue 4,  2007, pp.597-615
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2007.29.4.597
Title & Authors
ON δgs-CLOSED SETS AND ALMOST WEAKLY HAUSDORFF SPACES
Park, Jin-Han; Song, Dae-Seob; Lee, Bu-Young;

Abstract
The aim of this paper is to introduce the class of $\small{{\delta}gs}$-closed sets and obtain characterizations of almost weakly Hausdorff spaces due to Dontchev and Ganster. We also introduce the notion of $\small{{\delta}gs}$-continuity and investigate the relationships between it and other types of continuity.
Keywords
$\small{{\delta}gs}$-closed sets;almost weakly Hausdorff spaces;$\small{{\delta}gs}$-continuous functions;
Language
English
Cited by
References
1.
D. Andrijevic, Semi-preopen sets, Mat. Vesnik 38 (1986), 24-32.

2.
S.P. Arya and T. Nour, Characterizations of s-normal spaces, Indian J. Pure Appl. Math. 21 (1990), 717-719.

3.
K. Balachandran, P. Sundaram and H. Maki, On generalized continuous maps in topological spaces, Mem. Fac. Sci. Kochi Univ. Ser. A (Math.) 12 (1991), 5-13.

4.
S.G. Crossley and S.K. Hildebrand, Semi-closure, Texas J. Sci. 22 (1971), 99-112.

5.
S.G. Crossley and S.K. Hildebrand, Semi-topological properties, Fund. Math. 74 (1972), 233-254.

6.
A.S. Davis, Indexed systems of neighborhood for general topological spaces, Amer. Math. Monthly, 68 (1961), 886-893.

7.
R. Devi, K. Balachandran and H. Maki, Semi-generalized homeomorphisms and generalized semi-homeomorphisms in topological spaces, Indian J. Pure Appl. Math. 26 (1995), 271-284.

8.
R. Devi, H. Maki and K. Balachandran, Semi-generalized closed maps and generalized semi-closed maps, Mem. Fac. Sci. Kochi Univ. Ser. A (Math.) 14 (1993), 41-54.

9.
J. Dontchev and M. Ganster, On ${\delta}$-generalized closed sets and $T_{3/4}$-spaces, Mem. Fac. Sci. Kochi Univ. Ser. A (Math.) 17 (1996), 15-31.

10.
J. Dontchev, I. Arokiarani and K. Balachandran, On generalized ${\delta}$-closed sets and almost weakly Hausdorff spaces, Questions Answers Gen. Topology 18 (2000), 17-30.

11.
W. Dunham, $T_{1/2}$-spaces, Kyungpook Math. J. 17 (1977), 161-169.

12.
M.S. Elnaschie, On the uncertainty of Cantorian geometry and two-slit experiment, Chaos, Soliton & Fractals 9 (1998), 517-529.

13.
M.S. Elnaschie, Quantum gravity from descriptive set theory, Chaos, Soliton & Fractals 19 (2004), 1339-1344.

14.
D.S. Jankovic, On some separation axioms and ${\theta}$-closure, Mat. Vesnik 32 (1980), 439-449.

15.
B.D. Khalimsky, Applications of connected ordered topological spaces in topology, Conference of Math. Department of Povolsia, 1970.

16.
B.D. Khalimsky, R. Kopperman and P.R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topol. Appl. 36 (1990), 1-17.

17.
T.Y. Kong, R. Kopperman and P.R. Meyer, A topological approach to digital topology, Amer. Math. Monthly 98 (1991), 901-917.

18.
V. Kovalevsky and R. Kopperman, Some topology-based image processing algorithms, Ann. New York Acad. Sci. 728 (1994), 174-182.

19.
B.Y. Lee, M.J. Son and J.H. Park, ${\delta}$-semiopen sets and its applications, Far East J. Math. Sci. 3 (2001), 745-759.

20.
N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41.

21.
N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo 19 (1970), 89-96.

22.
A.S. Mashhour, M.B. Abd El-Monsef and S.N. El-Deeb, On precontinuous and weak precontinuous functions, Proc. Math. Phys. Soc. Egypt 53 (1982). 47-53.

23.
M. Mrsevic, I.L. Reilly and M.K. Vamanamurthy, On semi-regularization properties, J. Austral. Math. Soc. (Ser. A) 38 (1985), 40-54.

24.
O. Njastad, On some classes of nearly open sets, Pacific J. Math. 15 (1965), 961-970.

25.
T. Noiri, On ${\delta}$-continuous functions, J. Korean Math. Soc. 16 (1980), 161-166.

26.
T. Noiri, A generalization of perfect functions, J. London Math. Soc. 17 (1978), 540-544.

27.
T. Noiri and V. Popa, Faintly m-continuous functions, Chaos, Soliton & Fractals 19 (2004), 1147-1159.

28.
J.H. Park, B.Y. Lee and M.J. Son, On ${\delta}$-semiopen sets in topological space, J. Indian Acad. Math. 19 (1997), 59-67.

29.
J.H. Park, D.S. Song and R. Saadati, On generalized ${\delta}$-semiclosed sets in topological spaces, Choas, Soliton & Fractals 33 (2007), 1329-1338.

30.
S. Raychaudhuri and N. Mukherjee, On ${\delta}$-almost continuity and ${\delta}$-preopen sets, Bull. Inst. Math. Acad. Sinica 21 (1993), 357-366.

31.
M.J. Son, On ${\delta}$-semiopen sets and ${\delta}$-semicontinuous functions, Ph. D. Thesis Dong-A Univ. Korea (1999).

32.
T. Soundararajan, Weakly Hausdorff spaces and the cardinality of topological spaces, General Topology and its Relations to Modern Anabis and Algebra III, Proc. Conf. Kanpur 1968, 301-306 (Academia, Prague, 1971).

33.
N.Y. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78 (1968), 103-118.