Open Journal Systems

On a type of generalized open sets

Bishwambhar Roy


In this paper, a new class of sets called μ-generalized closed (briefly μg-closed) sets in generalized topological spaces are introduced and studied. The class of all μg-closed sets is strictly larger than the class of all μ-closed sets (in the sense of Á. Császár). Furthermore, g-closed sets (in the sense of N. Levine) is a special type of μg-closed sets in a topological space. Some of their properties are investigated here. Finally, some characterizations of μ-regular and μ-normal spaces have been given.


μ-open set; μg-closed set; μ-regular space; μ-normal space

Full Text:



M. E. Abd El-Monsef, S. N. El-Deeb and R. A. Mahmoud, B-open sets and B-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12 (1983), 77–90.

S. P. Arya and T. M. Nour, Characterizations of s-normal spaces, Indian J. Pure Appl. Math. 21, no. 8 (1990), 717–719.

Y. Beceren and T. Noiri, Some functions defined by semi-open sets and B-open sets, Chaos Solitons Fractals 36 (2008), 1225–1231.

P. Bhattacharyya and B. K. Lahiri, Semi-generalized closed sets in topology, Indian J. Math. 29 (1987), 376–382.

M. Caldas, T. Fukutake, S. Jafari and T. Noiri, Some applications of d-preopen sets in topological spaces, Bull. Inst. Math. Acad. Sinica 33, no. 3 (2005), 261–275.

M. Caldas, D. N. Georgiou and S. Jafari, Characterizations of low separation axioms via a-open sets and a-closure operator, Bull. Soc. Paran. Mat. (3)21 (2003), 97–111.

M. Caldas, D. N. Georgiou and T. Noiri, More on -semiopen sets, Note di Mathematica

, no. 2 (2003), 113–126.

M. C. Caldas and S. Jafari, On d D-sets and associated weak separation axioms, Bull. Malaysian Math. Soc. 25 (2002), 173–185.

Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), 351–357.

Á. Császár, Generalized open sets in generalized topologies, Acta Math. Hungar. 106 (2005), 53–66.

Á. Császár, d- and 0-modifications of generalized topologies, Acta Math. Hungar. 120 (2008), 275–279.

Á. Császár, Normal generalized topologies, Acta Math. Hungar. 115, no. 4 (2007), 309– 313.

J. Dontchev, I. Arokiarani and K. Balachandran, On generalized d-closed sets and almost weakly Hausdroff spaces, Questions Answers Gen. Topology 18, no. 1 (2000), 17–30.

C. Dorsett, Semi normal spaces, Kyungpook Math. J. 25(1985), 173–180.

C. Dorsett, Semi regular spaces, Soochow J. Math. 8 (1982), 45–53.

J. Dugunji, Topology, Allyn and Bacon, Boston, 1966.

E. Ekici, On y-normal spaces, Bull. Math. Soc. Sci. Math. Roumanie 50 (98) (2007), 259–272.

E. Ekici, On almost ngp-continuous functions, Chaos Solitons Fractals 32 (2007), 1935– 1944.

S. Jafari and T. Noiri, On B-quasi irresolute functions, Mem. Fac. Sci. Kochi Univ.(Math.) 21 (2000), 53–62.

A. Kar and P. Bhattacharyya, Bitopological a-compact spaces, Riv. Mat. Parma 7, no. 1 (2002), 159–176.

A. Keskin and T. Noiri, On bD-sets and associated separation axioms, Bull. Iran. Math. Soc. 35, no. 1 (2009), 179–198.

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

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

S. N. Maheshwari and R. Prasad, On s-regular spaces, Glasnik Mat. 10 (30) (1975), 347–350.

H. Maki, J. Umehara and T. Noiri, Every topological space is pre-T1/2, Mem. Fac. Sci. Kochi Univ. Ser. A. Math. 17 (1996), 33–42.

H. Maki, J. Umehara and K. Yamamura, Characterizations of T1/2-spaces using generalized v-sets, Indian J. Pure Appl. Math. 19, no. 7 (1998), 634–640.

H. Maki, R. Devi and K. Balachandran, Associated topologies of generalizrd a-closed sets and a-generalized closed sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math. 15 (1994), 51–63.

H. Maki, R. Devi and K. Balachandran, Generalized a-closed sets in topology, Bull. Fukuoka Univ. Ed., Part-III 42 (1993), 13–21.

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.

T. Noiri, Semi-normal spaces and some functions, Acta Math. Hungar. 65, no. 3 (1994), 305-311.

M. C. Pal and P. Bhattacharyya, Feeble and strong forms of preirresolute functions, Bull. Malaysian Math. Soc. 19 (1996), 63–75.

J. H. Park, D. S. Song and R. Saadati, On generalized d-semiclosed sets in topological spaces, Chaos Solitons Fractals 33 (2007), 1329–1338.

S. Raychaudhuri and M. N. Mukherjee, On d-almost continuity and d-preopen sets, Bull. Inst. Math. Acad. Sinica 21 (1993), 357–366.

P. Sivagami and D. Sivaraj, W and V- sets of generalized topologies, Scientia Magna 5, no. 1 (2009), 83–93.

N. V. Velicko, H-closed topological spaces, Mat. Sb. 70 (1966), 98–112.

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM


  • There are currently no refbacks.