γ*-OPERATION IN THE PRODUCT
OF TOPOLOGICAL SPACES
Shukri Haxha1, Qefsere Doko Gjonbalaj2
1,2Faculty of Electrical and Computer Engineering
Department of Mathematics
University of Prishtina ``Hasan Prishtina''
Prishtinë, 10 000, KOSOVË

Abstract

In this paper, we define the concept of $\gamma ^{*}$-operation in the topological product of topological spaces $(X_{i},\mathcal {T}_{i}), i \in I$, through $\gamma_{i}$-operations of spaces $(X_{i},\mathcal {T}_{i}), i \in I$. In addition, we examine whether the product of $\gamma_{i}$-open sets from $(X_{i},\mathcal {T}_{i}), i \in I$ spaces, is a $\gamma ^{*}$-open set in the topological product of these spaces. Further, we examine the $\gamma ^{*}$-continuity of projections $p_i: \prod_{i\in I} X_{i}\rightarrow X_{i}$. Also we prove, whether the product of $\gamma_{i}-T_{0}$ spaces, $\gamma_{i}-T_{1}$ spaces and $\gamma_{i}$-Hausdorff's spaces, is $\gamma^{*}-T_{0}$ space, $\gamma^{*}-T_{1}$ space or $\gamma ^*$-Hausdorff space, respectively.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 4
Year: 2018

DOI: 10.12732/ijam.v31i4.11

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