ON An Infra-\(\alpha\)-Open Sets
About this article
Abstract
In this paper, we define a new class of set in general topology called an infra- \(\alpha\) open set and we investigate fundamental properties by using this new class. The relation between infra-\(\alpha\)-open set and other topological sets are studied.
Moreover, In the light of this new definition, we also define some generalization of continuous mappings and discuss the relations between these new classes of mappings and other continuous mappings. Basic properties of these new mappings are studied and we apply these new classes to give characterization of connected space.
Keywords
- infra-\(\alpha\) -open set
- infra-\(\alpha\)-closed set
- infra-\(\alpha\)-continuous mapping
- infra-\(\alpha\)-open mapping
- infra \(\alpha\)-closed mapping
- infra-\(\alpha\)- irresolute
- infra-\(\alpha\)-connected
References
[1] W. Dunham, ”A New Closure Operator for non-T1 topology”, Kyuungpook Math. J., 22(1982), pp. 55-60.
[2] N. Levine, ”semi open sets and semi-continuouity in topological space”, Amer. Math. Monthly, 70(1) (1981), pp.36-41.
[3] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deed, ”On Precontinuous and weak precontinuous Mappings”, Proc. Math. Phys. Soc. Egypt, 53 (1982), pp.47-53.
[4] O. Njastad, ”Some Classes of Nearly Open sets”, Pacific J. Math., 15(3)(1965), pp. 961-970.
[5] S. Pious Missier and P. Anbarasi Rodrigo, ”Some Notions of Nearly Open Sets in Toological Spaces”, Intenational Journal of Mathematical Archive, 4(12) (2013) 12-18.
[6] A. Robert and S. Pious Missier, ”A New Class of Nearly Open Sets”, Intenational Journal of Mathematical Archive, 3(7) (2012) 2575- 2582.
[7] T. Selvi and A. Punitha Dharani, ”Some new class of nearly closed and open sets”, Asian Journal of Current Engineering and Maths, 1 : 5 Sep Oct (2012) 305-307.