Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2015, 3(4), 108-110
DOI: 10.12691/tjant-3-4-4
Open AccessArticle

Generalized s-topological Groups

Rehman Jehangir1, and Moizud Din Khan2,

1Department of Mathematics, Preston University Kohat (Islamabad), Pakistan

2Department of Mathematics, COMSATS institute of information technology, Chak Shehzad Islamabad, Pakistan

Pub. Date: November 26, 2015

Cite this paper:
Rehman Jehangir and Moizud Din Khan. Generalized s-topological Groups. Turkish Journal of Analysis and Number Theory. 2015; 3(4):108-110. doi: 10.12691/tjant-3-4-4

Abstract

In this paper, we explore the notion of generalized semi topological groups. This notion is based upon the two ideas, generalized topological spaces introduced by Csaszar [2,3] and the semi open sets introduced by Levine [7]. We investigate on the notion of generalized topological group introduced by Hussain [4]. We explore the idea of Hussain by considering the generalized semi continuity upon the two maps of binary relation and inverse function.

Keywords:
generalized semi open sets generalized compact sets generalized continuity generalized continuity generalized discrete sets

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References:

[1]  E. Bohn, J. Lee, Semi-topological groups, Amer. Math. Monthly 72 (1965), 996.998.
 
[2]  Á. Császár, Generalized open sets, Acta Math. Hungar., 75 (1997), 65-87.
 
[3]  Á. Császár, Generalized topology, generalized continuity, Acta Math.Hungar., 96 (2002), 351-357.
 
[4]  M. Hussain, M. Khan and C. Ozel, On generalized topological groups, Filomat, 2013 27(4):567-575.
 
[5]  M. Hussain, M. Khan and C. Ozel, More on generalized topological groups, Creative Math. & Inf. 22(2013)(1), 47-51.
 
[6]  M. Hussain, M. Khan, A, Z, Özcelik, and C. Ozel, Extension closed properties on generalized topological groups, Arab J Math (2014) 3:341-347.
 
[7]  N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36.41.1.
 
[8]  Michel Coste, Real Algebraic Sets, March 23, 2005.
 
[9]  J. Cao, R. Drozdowski, Z. Piotrowski, Weak continuity properties of topologized groups, Czech. Math. J., 60 (2010), 133-148.
 
[10]  C. Silva and R. Silva, On generalized S topological group, International journal of science and research, 6, (2015), 1-4.