On Fuzzy α̂g-Topological R-Module Spaces

The aim of this research is to give a new definition and study a new notion of fuzzy α̂g-topological R-module spaces using fuzzy α̂g-open sets. The concept of fuzzy α̂g-topological R-modules is introduced and study them to provide a mathematical basis. Traditional cautiousness for F bisected by α̂g-tautologies reigns furtive-space yield we assay different fuzzy α̂g-separation axioms such as  where  in the context of these spaces.  Also, we study fuzzy -separation axiom  in fuzzy  - Topological. R-Module space. The results indicate that throughout the  domain of a fuzzy topological R-module space  the following fuzzy separation axioms  and are valid.  Also, we also show that possessing fuzzy α̂g-open neighborhoods has further consequences to the structure and continuity of fuzzy topological spaces. The main conclusion of our research is that the mysterious α̂g topological R-unit spaces are a new and interesting area for further study. The terms of their operations in addition to providing important information about the interaction between fuzziness and topological properties that may be useful in many mathematical and applied branches.