Sobriety in Fuzzy Topology
by
Dexue Zhang
Department of Mathematics, SichuanUniversity, Chengdu 610064, China

A phenomenon which sharply distinguishes fuzzy topology from classical topology is that the construct L-FTS of L-fuzzy topological spaces has non-trivial full subconstructs which are concretely both reflective and coreflective. Each such subconstruct is closed with respect to final and initial structures in L-FTS, and thus, gives rise to a natural autonomous theory of topology. Thus it can be said, to some extent, that fuzzy topology should consist of a system of closely related topology theories with each applying to a both finally and initially closed full subconstruct of L-FTS. In this paper we present an example, in the case L is a linearly ordered complete lattice, to illustrate this idea by introducing sobriety for each such subconstruct, including the sobriety of crisp topological spaces as a special case.

Date received: March 21, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeq-02.