Quantale-valued fuzzy Scott topology

Document Type: Research Paper

Authors

1 Department of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-City Jeonbuk, 561-756, Republic of Korea

2 Department of Mathematics, College of Natural Science, Chonbuk National University, Jeonju-City Jeonbuk, 561-756, Republic of Korea and School of Mathematics and Science, Hebei GEO University, Shijiazhuang 050018, China

3 School of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, P.R. China

Abstract

The aim of this paper is to extend the truth value table of
lattice-valued convergence spaces to a more general case and
then to use it to introduce and study the quantale-valued fuzzy Scott
topology in fuzzy domain theory. Let $(L,*,\varepsilon)$ be a
commutative unital quantale and let $\otimes$ be a binary operation
on $L$ which is distributive over nonempty subsets. The quadruple
$(L,*,\otimes,\varepsilon)$ is called a generalized GL-monoid if
$(L,*,\varepsilon)$ is a commutative unital quantale and the operation $*$ is
$\otimes$-semi-distributive. For generalized GL-monoid $L$ as the
truth value table, we systematically propose the stratified
$L$-generalized convergence spaces based on stratified $L$-filters,
which makes various existing lattice-valued convergence spaces as
special cases. For $L$ being a commutative unital quantale, we
define a fuzzy Scott convergence structure on $L$-fuzzy dcpos and
use it to induce a stratified $L$-topology. This is the inducing way
to the definition of quantale-valued fuzzy Scott topology, which
seems an appropriate way by some results.

Keywords


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