Strongly \({g^{*}}\)-Closed Graph Function with Strongly-\({T_{i}{^{g^{*}}}}\) Spaces

K. Sivakumar, T. Arunachalam, R. Parimelazhagan

Abstract


In this paper, we introduce the graph function called Strongly \(g^{*}\)-closed graph function and studied some of their properties.


Keywords


Strongly \(g^{*}\)-closed graph function

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References


D. Andrijevic, On b-open sets, Mat. Vesink 48 (1996), 59 – 64.

D. Andrijevic, Semi-preopen sets, Mat. Vesink 38 (1986), 24 – 32.

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

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.

P. Bhattacharyya and B. K. Lahiri, Semi-generalizsed closed sets in topology, Indian J. Math. 29 (1987), 375 – 382.

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.

D. E. Cameron, Some maximal topologies which are Q.H.C., Proc. Amer. Math. Soc. 75 (1979), 149 – 156, DOI: 10.1090/S0002-9939-1979-0529232-8.

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.

A. A. El-Atik, A Study on Some Types of Mappings on Topological Spaces, M.Sc. thesis, Tanta University, Egypt (1997).

E. Ekici and M. Caldas, Slightly gamma-continuous functions, Bol. Soc. Paran. Mat. 22 (2004), 63 – 74.

M. Ganster and I. L. Reilly, Locally closed sets and LC-continuous functions, Internat. J. Math. Math. Sci. 12(3) (1989), 417 – 424, DOI: 10.1155/S0161171289000505.

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, DOI: 10.1080/00029890.1963.11990039.

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.

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.

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

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, DOI: 10.2140/pjm.1965.15.961.

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

R. Parimelazhagan, Strongly Tg* k -spaces, Journal of Informatics and Mathematical Sciences 11(2) (2019), 147 – 154, DOI: 10.26713/jims.v11i2.958.

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.

R. Parimelazhagan, Strongly g*d#-sets in topological spaces, (submitted).

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.

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

J. Tong, A decomposition of continuity, Acta Math. Hungar. 48 (1986), 11 – 15, DOI: 10.1007/BF01949045.

J. Tong, On decomposition of continuity in topological spaces, Acta Math. Hungar. 54 (1-2) (1989), 51 – 55, DOI: 10.1007/BF01950708.

A. Wilansky, Between T1 and T2, Amer. Math. Monthly 74 (1967), 261 – 266, DOI: 10.1080/00029890.1967.11999950.




DOI: http://dx.doi.org/10.26713%2Fjims.v11i3-4.930

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