Constructions in the category of fuzzy T-proximity spaces

This paper is devoted to study the initial fuzzy T-proximity structures of the fuzzy T-proximity spaces defined by Hashem and Morsi in 2002, where T stands for any continuous triangular norm. In this paper, we show that all initial and final lifts in the category T-FPS of these fuzzy T-proximity spaces exist and hence the initial and final fuzzy T-proximity structures exist. We introduce a characterization for the initial fuzzy T-proximity structures, so as a special initial fuzzy T-proximity spaces, the subspaces and product spaces of these fuzzy T-proximity spaces can also be characterized. We also show that the fuzzy topology associated to the initial fuzzy T-proximity structure of a family of fuzzy T-proximity spaces, coincides with the initial fuzzy topology of the family of fuzzy topologies associated to these fuzzy T-proximity spaces.