Abstract
In this paper, the notion of M-fuzzifying convex remotehood systems is introduced and characterizations of M-fuzzifying convex spaces are obtained. Further, notions of remote mappings and M-fuzzifying convex quasi-uniformities are introduced. It is proved that M-fuzzifying convex quasi-uniform space and M-fuzzifying convex space are mutually induced. In order to discuss categorical relationships among M-fuzzifying convex quasi-uniform spaces, M-fuzzifying convex remotehood spaces and M-fuzzifying convex spaces, notions of M-fuzzifying quasi-uniformizable convex structures and M-fuzzifying quasi-uniformizable convex remotehood spaces are presented. It is proved that the category of M-fuzzifying quasi-uniformizable convex spaces and the category of M-fuzzifying quasi-uniformizable convex remotehood spaces can be embedded into the category of M-fuzzifying convex quasi-uniform spaces as subcategories.
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