A study on hereditary generalized regular submaximal spaces
Keywords:
Dense-H-sets, Hereditary generalized submaximal space, g-H-open, Pre regular-H-open set, Regular-H-closed
Abstract
In this paper the concepts of dense--sets, codense--sets, hereditary generalized submaximal spaces and hereditary generalized regular submaximal spaces are introduced with necessary examples. Also interesting properties and some equivalent statements of hereditary generalized regular submaximal spaces are discussed.
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References
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Kirch M.R., On Hecuitt’s τ-maximal spaces, J. Austral Math. Soc. 14 (1972) 45-48.
Levine N., Generalized Closed Sets in Topology, Rend. Circ. Mat. Palermo, 19 (2) (1970), 89-96.
Njåstad O., On Some Classes of Nearly Open Sets, Pacific J. Math., 15 (1965), 961- 970.
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Zaitsav V., On Certain Classes of Topological Spaces and their Bicompactifications, Dokl. Akad Nauk SSSR, 178(1979), 778-779.
Acikgoz A., Yuksel S. and Noiri T., α-I-preirresolute functions and β-I-preirresolute functions, Bull. Malays. Math. Sci. Soc. (2) (28), (1) (2005), 1- 8.
Alas O. T, Sanchis M., Thacenko M. G., Thachuk V.V. and Wilson R.G., Irresolvable and submaximal spaces, Homogeneity versus ¾-discreteness and new ZFC examples, Topology Appl., 107 (2000), 259-273.
Arhangelski A.V., and Collins P.J., On submaximal spaces, Topology Appl., 64 (3) (1995), 219-241.
Balachandran K., Sundaram P. and Maki H., Generalised Locally Closed Sets and GLC-Continuous Functions, Indian J. Pure and Appl. Math., 27(3)(1996), 235 -244.
Bhavani K. and Sivaraj D., Ig-Submaximal Spaces, Bol. Soc. Paran. Mat. (3s.) v. 331 (2015): 103–108.
Bourbaki N., Topologic Generale, 3rded., Actualities Scientifiques at Industrielles 1142 (Hermann, paris, 1961).
Chandrasekhara Rao K., Topology, Narosa Publishing House, New Delhi.
Csaszar A., Generalized Open Set in Generalized Topologies, Acta Math. Hungry. 2005; 106(1-2): 53-66.
Csaszar A., Modification of Generalized Topologies via Hereditary Classes, Acta Math. Hungry 115 (2007),29-36.
Ekici E. and Noiri T., Properties of I-submaximal ideal topological spaces, Filomat, 24 (4) (2010), 87-94.
Guthrie J.A., Stone H.E. and Wage M.L., Maximal Connected Hausdroff Topologies, Topology Proc. 2(1977), 349-353.
Hewitt E., A problem of Set-Theoretic Topology, Duke Math. J., 10 (1943), 309-333.
Indirani K., Sathishmohan P. and Rajendran V., On GR*- Continuous Functions in Topological Spaces, International Journal Of Science, Engineering and Technology Research (Ijsetr), Volume 3, Issue 4, April 2014.
James R. Munkers, Topology, Prentice Hall of India Private Limited, New Delhi, (1984).
Julian Dontchev, Between A- and B-sets*, University of Helsinki, Department of Methematics, Finland, [math. GN] 1 Nov 1998.
Katetov M., On Spaces which do not have disjoint dense subspaces, Mat. Sb. 21 (1947) 3-12.
Kirch M.R., On Hecuitt’s τ-maximal spaces, J. Austral Math. Soc. 14 (1972) 45-48.
Levine N., Generalized Closed Sets in Topology, Rend. Circ. Mat. Palermo, 19 (2) (1970), 89-96.
Njåstad O., On Some Classes of Nearly Open Sets, Pacific J. Math., 15 (1965), 961- 970.
Sheik John M., On w-Closed Sets in Topology, Acta Ciencia India, 4(2000), 389-392.
Stone M., Application of the Theory of Boolean Rings to General Topology, Trans. Amer. Math. Soc., 41(1937), 374 – 481.
Zaitsav V., On Certain Classes of Topological Spaces and their Bicompactifications, Dokl. Akad Nauk SSSR, 178(1979), 778-779.
Published
2017-04-11
How to Cite
Amudhambigai, B., Madhuri, V., & Rowthri, M. (2017). A study on hereditary generalized regular submaximal spaces. Journal of Advanced Mathematics, 3(1), 01-03. Retrieved from https://asdpub.com/index.php/jam/article/view/319
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