POINT SPACES FOR FUZZY TOPOLOGICAL-SPACES

We define a category F of fuzzy topological spaces whose objects are the pairs (L, τ), where L is any distributive lattice with universal bounds 0 and 1, 0≠1, and τ is a fuzzy topology on L and whose morphisms u: L1 →L2 are relations such that u-1: L2→L1 is a lattice homomorphism. We define a covariant functor *: F→T, where T is the category of fuzzy topological spaces. The points of the topological spaces *(L, τ) are called fuzzy points of (L, τ), and allow us to define local topological concepts which depend on a base for a topology. We have natural functors from the Hutton category H, from the Chang-Goguen category C G(L), from the Lowen category L and from the Rodabaugh category FUZZ into F. © 1990.