2 TYPES OF STABLE SUBCONSTRUCTS OF FTS

In the topological construct FTS of fuzzy topological spaces and conti nuous functions, the subconstructs T-FLS, of fuzzy T-locality spaces, and T-FNS, of fuzzy T-neighborhood spaces, are simultaneously bireflec tive and bicoreflective in FTS for certain infinite sets of triangular norms T. We identify their stabilizing, total fuzzy topologies Omega( T-FLS) and Omega(T-FNS) on [0, 1] in the sense of R. Lowen and P. Wuyt s (J. Fuzzy Mathematics 1:475-489 (1993)). (The special case of T = Mi n has already been dealt with by Lowen and Wuyts.) We also establish a symmetrically-defined, order-reversing bijection between Omega(T-FNS) and a basis for Omega(T-FLS).