On Various $g$-Topology in Statistical Metric Spaces

Year 2019, Volume: 2 Issue: 3, 107 - 115, 30.09.2019

V. Renukadevi , S. Vadakasi

https://doi.org/10.32323/ujma.561120

Cited By: 1

Abstract

The purpose of this paper is to analyze the significance of new $g$-topologies defined in statistical metric spaces and we prove various properties for the neighbourhoods defined by Thorp in statistical metric spaces. Also, we give a partial answer to the questions, namely "What are the necessary and sufficient conditions that the $g$-topology of $type V$ to be of $type V_{D}?,$ the $g$-topology of $type V_{\alpha}$ to be the $g$-topology of $type V_{D} ?$ and the $g$-topology of $type V_{\alpha}$ to be a topology?" raised by Thorp in 1962. Finally, we discuss the relations between $\M_{\Omega}$-open sets in generalized metric spaces and various $g$-topology neighbourhoods defined in statistical metric spaces. Also, we prove weakly complete metric space is equivalent to a complete metric space if $\Omega$ satisfies the $\mathcal{V}$-property. 

Keywords

SM space, type V_D, g-ecart-topology, R-g-topology

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