ON An Infra-\(\alpha\)-Open Sets

Authors

  • Hakeem Othman

    Head of Department of Mathematics, Al-Qunfudah Center for ScientificResearch,\\ AL-Qunfudhah University college, Umm Al-Qura University,KSA.

  • Md.Hanif. Page

    Department of Mathematics, BVB College of Engineering and Technology,, Hubli-580031. Karnataka State, India.

Received date: April 15, 2016

Accepted date: April 16, 2016

Published date: April 19, 2016

DOI:

https://doi.org/10.14419/gjma.v4i3.6124

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

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.

References

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    [2] N. Levine, â€semi open sets and semi-continuouity in topological spaceâ€, Amer. Math. Monthly, 70(1) (1981), pp.36-41.

    [3] A. S. Mashhour, M. E. Abd El-Monsef and S. N. El-Deed, â€On Precontinuous and weak precontinuous Mappingsâ€, Proc. Math. Phys. Soc. Egypt, 53 (1982), pp.47-53.

    [4] O. Njastad, â€Some Classes of Nearly Open setsâ€, Pacific J. Math., 15(3)(1965), pp. 961-970.

    [5] S. Pious Missier and P. Anbarasi Rodrigo, â€Some Notions of Nearly Open Sets in Toological Spacesâ€, Intenational Journal of Mathematical Archive, 4(12) (2013) 12-18.

    [6] A. Robert and S. Pious Missier, â€A New Class of Nearly Open Setsâ€, Intenational Journal of Mathematical Archive, 3(7) (2012) 2575- 2582.

    [7] T. Selvi and A. Punitha Dharani, â€Some new class of nearly closed and open setsâ€, Asian Journal of Current Engineering and Maths, 1 : 5 Sep Oct (2012) 305-307.

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How to Cite

Othman, H., & Page, M. (2016). ON An Infra-\(\alpha\)-Open Sets. Global Journal of Mathematical Analysis, 4(3), 12-16. https://doi.org/10.14419/gjma.v4i3.6124

Received date: April 15, 2016

Accepted date: April 16, 2016

Published date: April 19, 2016