Some Properties of θ-sgp-Neighbourhoods

Md. Hanif PAGE1; V.T.Hosamath

doi:https://doi.org/10.14445/22315373/IJMTT-V20P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 20 | Number 1 | Year 2015 | Article Id. IJMTT-V20P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V20P506

Some Properties of θ-sgp-Neighbourhoods

Md. Hanif PAGE1, V.T.Hosamath

Abstract

A new generalized closed set called θ-sgp-closed set is introduced in[8]. In this paper, we continue the study of θ-sgp-closed set. Using this set we define the concepts of θ-sgp-neighbourhoods, θ-sgp-limit points, θ-sgp-derived sets, θ-sgp-Ro and θ-sgp-R1 spaces in topological spaces. We also introduce and study the concept of θ-sgp-closure, θ-sgp-interior and θ-sgp-kernel in topological spaces by using the notion of θ-sgp-closed sets and investigate some of their properties.

Keywords

θ-sgp-closed set, θ-sgp-open set, θ-sgp-nbd, θ-sgpd(A), θ-sgpCl(A), θ-sgpInt(A), θ-sgp-Ro, θ-sgp-R1.

References

[1] Miguel Caldas and Saeid Jafari, On θ-semigeneralized closed sets in topology, Kyungpook Math J. 43(2003), 135-148.
[2] S . G. Crossely and S. K. Hildbrand, On semi-closure, Texas J. Sci, 22(1971), 99-112.
[3] N. El-Deeb, I. A. Hasanein, A. S. Mashhour and T. Noiri, On p-regular spaces, Bull. Math. Soc.
Sci. Math. R.S. Roumanie, 22(75)(1983), 311-315.
[4] N. Levine, Generalized closed sets in topology, Rend. Circ. Math. Paleomo 19(1970), 89-96.
[5] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70(1963), 36-41.
[6] 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.
[7] G.B. Navalagi and Md. Hanif PAGE, On θgs-Neighbourhoods ,Indian Journal of Mathematics and Mathematical Sciences, Vol. 4, No.1, (2008), pp 1-11.
[8] Md. Hanif PAGE and V. T. Hosamath, On θ-Semigeneralized pre closed sets in topological spaces, Int. Journal of Scientific and Mathematical Research, Vol.3, (3)(2015), 74-80.
[9] M.C. Pal and P. Bhattacharyya, Feeble and strong forms of pre-irresolute functions, Bull. Malaysian Math. Soc., 19(1996), 63-75.

Citation :

Md. Hanif PAGE1, V.T.Hosamath, "Some Properties of θ-sgp-Neighbourhoods," International Journal of Mathematics Trends and Technology (IJMTT), vol. 20, no. 1, pp. 47-54, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V20P506