On $\beta-$topological vector spaces

Document Type: Research Paper

Authors

1 Department of Mathematics, University of Jammu, JK-18006, India

2 Department of Mathematics, University of Jammu, JK-18006, India.

Abstract

We introduce and study a new class of spaces, namely $\beta-$topological vector spaces via $\beta-$open sets. The relationships among these spaces with some existing spaces are investigated. In addition, some important and useful characterizations of $\beta-$topological vector spaces are provided.
 

Keywords

Main Subjects


[1]  M. E. Abd El-Monsef, S. N. El-Deep, R. A. Mahmond, β−open sets and β−continuous mappings, Bull. Fac.
Sci. Assiut. Univ. 12 (1983), 77-90.

[2]  Y. A. Abou-Elwan, Some properties of β−continuous mappings, β−open mappings and β−homeomorphism, Middle-East J. of Sci. Res. 19 (12) (2014), 1722-1728.

[3]  H. Z. Ibrahim, α−topological vector spaces, Sci. J. Uni. Zakho. 5 (1) (2017), 107-111.

[4]  M. D. Khan, S. Azam, M. S. Bosan, s-topological vector spaces, J. Linear. Topological. Algebra. 4 (2) (2015), 153-158.

[5]  M. Khan, M. I. Iqbal, On irresolute topological vector spaces, Adv. Pure. Math. 6 (2016), 105-112.

[6]  N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly. 70 (1963), 36-41.

[7] O. Njastad, On some classes of nearly open sets, Paci c. J. Math. 15 (1965), 961-970.