The study examines the categorical connections of [Formula: see text]-G-filters with [Formula: see text]-filters and [Formula: see text]-interior operators. Besides, the relationship between [Formula: see text]-G-filters and [Formula: see text]-fuzzy pre-proximities is also explored. Indeed, the Galois correspondence between the categories of stratified [Formula: see text]-G-filter spaces and [Formula: see text]-fuzzy pre-proximity spaces is revealed in this paper.
In this paper, the authors introduce catalyzed LM-G-filter spaces, a special case of weakly inspired LM-G-filter spaces and identify certain properties of these spaces. It is proved that C LM-G, the category of catalyzed LM-G-filter spaces, is isomorphic to I LM-G, the category of inspired LM-G-filter spaces. Moreover, the categorical connection between WI LM-G, the category of weakly inspired LM-G-filter spaces, and C LM-G is investigated through interior and exterior catalyzation of weakly inspired LM-G-filter spaces. It is proved that C LM-G is an isomorphism-closed, bireflective and bicoreflective full subcategory of WI LM-G and LM-G.
This paper presents the idea of Alexandrov L-quasi-G-filter space and examines its relationship with L-fuzzy relations. It is proved that every Alexandrov L-quasi-G-filter induces an L-fuzzy relation and vice-versa. By identifying certain functors, the study has brought out the connections between the categories of Alexandrov L-quasi-G-filter spaces and Alexandrov L-fuzzy pre-uniform spaces. Further, the study has explored and thereby establishes the scope of Alexandrov L-quasi-G-filter spaces in mathematical modeling and decision-making processes.
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