@article{article_561120, title={On Various $g$-Topology in Statistical Metric Spaces}, journal={Universal Journal of Mathematics and Applications}, volume={2}, pages={107–115}, year={2019}, DOI={10.32323/ujma.561120}, author={Renukadevi, V. and Vadakasi, S.}, keywords={SM space,type V_D,g-ecart-topology,R-g-topology}, abstract={<p style="text-align:justify;"> <span style="font-size:14px;">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.  </span> <br /> </p>}, number={3}, publisher={Emrah Evren KARA}