### Strongly \(T_{k}{^{g^{*}}}\)-Spaces

#### Abstract

In this paper, we introduce the spaces called Strongly-\(T_{0}{^{g^{*}}}\)-space, Strongly-\(T_{1}{^{g^{*}}}\)-space and Strongly-\(T_{2}{^{g^{*}}}\) in topological spaces. Also, we introduce Strongly \(g^{*}\)-symmetric and studied some of their properties.

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D. Andrijevic, Semi-preopen sets, Mat. Vesink 38 (1986), 24 – 32, https://eudml.org/doc/259773.

I. Arockiarani, Studies on Generalizations of Generalized Closed Sets and Maps in Topological Spaces, Ph.D Thesis, Bharathiar University, Coimbatore (1997), http://hdl.handle.net/10603/101249.

S. P. Arya and M. P. Bhamini, A note on semi-US spaces, Ranchi Uni. Math. J. 13 (1982), 60 – 68.

C. E. Aull, Sequences in topological spaces, Comm. Math. (1968), 329 – 336.

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

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

R. Devi, Studies on Generalizations of Closed Maps and Homeomorphisms in Topological Spaces, Ph.D Thesis, Bharathiar University, Coimbatore (1994), http://hdl.handle.net/10603/102774.

Y. Gnanambal, On generalized pre-regular closed sets in topological spaces, Indian J. Pure Appl. Math. 28 (1997), 351 – 360.

N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Palermo 19 (1970), 89 – 96, DOI: 10.1007/BF02843888.

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

P. E. Long and L. L. Herington, Basic properties of regular closed functions, Rend. Cir. Mat. Palermo 27 (1978), 20 – 28, DOI: 10.1007/BF02843863.

S. R. Malghan, Generalized closed maps, J. Karnataka Univ. Sci. 27 (1982), 82 – 88.

A. S. Mashhour, I. A. Hasanein and S. N. El-Deeb, (alpha)-continuous and (alpha)-open mappings, Acta Math. Hung. 41 (1983), 213 – 218, DOI: 10.1007/BF01961309.

A. S. Mashhour, M. E. Abd EI-Monsef and S. N. EI-Deeb, On precontinuous and weak pre-continuous mapping, Proc. Math., Phys. Soc. Egypt 53 (1982), 47 – 53.

N. Nagaveni, Studies on Generalizations of Homeomorphisms in Topological Spaces, Ph.D Thesis, Bharathiar University, Coimbatore (1999).

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

R. Parimelazhagan and V. S. Pillai, Strongly (g^*)-closed sets in topological spaces, Int. Journal of Math. Anal. 6 (30) (2012), 1481 – 1489.

R. Parimelazhagan, More on strongly (g^*)-open sets in topological spaces, unpublished.

M. K. Singal and A. R. Singal, Almost-continuous mappings, Yokohama Math. J. 16 (1968), 63 – 73.

V. S. Pillai and R. Parimelazhagan, On strongly (g^*)-continuous maps and pasting lemma in topological spaces, International Journal of Computer Applications 63 (6) (2013), 46 – 48, DOI: 10.5120/10474-5191.

V. S. Pillai and R. Parimelazhagan, Strongly (g^*)-irresolute and homeomorphism in topological spaces, International Journal of Recent Scientific Research 4(1) (2013), 005 – 007.

A. Wilansky, Between (T_1) and (T_2), Amer. Math. Monthly 74 (1967), 261 – 266, DOI: 10.1080/00029890.1967.11999950.

DOI: http://dx.doi.org/10.26713%2Fjims.v11i2.956

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