Fuzzy topological spaces associated to L-filters.
by
Carlos Ochoa-Castillo
Universidad Distrital Francisco José de Caldas
Coauthors: Joaquín Luna-Torres (Universidad Sergio Arboleda, Bogotá, Colombia)

In the context of U. Höhle and A. P. Sostak in ``Axiomatic Fundations of Fixed-Basis Fuzzy Topology" (Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, edited by U. Höhle and S. E. Rodabaugh, Chapter 3, Kluwer Academic Publishers, Boston/Dodrecht/London, 1999), we explore the relations between L-filters and L-fuzzy topological spaces, for L a residuated complete quasi-monoidal lattice. Namely, we point out that:

1. Every L-filter induces, in a natural way, a L-fuzzy topology.
2. There exists a functor from the category L-FIL, of the L-filters and filter-continuos maps, to the category L-FTOP of L-fuzzy topological spaces and LF-continuos maps.
3. It is possible to change basis L for L-fuzzy topologies associated to L-filters.
4. For each extensional L-filter, the associated L-fuzzy topology is extensional.

Date received: January 29, 2001

Copyright © 2001 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 # cafw-10.