We define and study a quantale-valued Wijsman structure on the hyperspace of all non-empty closed sets of a quantale-valued metric space. We show its admissibility and that the metrical coreflection coincides with the quantale-valued Hausdorff metric and that, for a metric space, the topological coreflection coincides with the classical Wijsman topology. We further define an index of compactnes...

It is well known that lattice-valued rough sets are important branches of fuzzy sets. The axiomatic characterization and related topology the main research directions For L=(L,⊛), a complete co-residuated lattice (CCRL), Qiao recently defined an L-fuzzy lower approximation operator (LFLAO) on basis relation. In this article, we give further study Qiao’s LFLAO around induced L-topology. Firstly,...

we study different completeness definitions for two categories of lattice-valued cauchy spaces and the relations between these definitions. we also show the equivalence of a so-called completion axiom and the existence of a completion.

This paper deals with a broad question—to what extent is topology algebraic—using two specific questions: (1) what are the algebraic conditions on the underlying membership lattices which insure that categories for topology and fuzzy topology are indeed topological categories; and (2) what are the algebraic conditions which insure that algebraic theories in the sense of Manes are a foundation f...

In this paper, we define a kind of lattice-valued convergence spaces based on the notion of $top$-filters, namely $top$-convergence spaces, and show the category of $top$-convergence spaces is Cartesian-closed. Further, in the lattice valued context of a complete $MV$-algebra, a close relation between the category of$top$-convergence spaces and that of strong $L$-topological spaces is establish...

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...

Introduction and motivation To explain the motivation of our work we give a short glimpse into the history of Fuzzy Topology called more recently Lattice-Valued Topology or Many Valued Topology. In 1968, C. L. Chang [1] introduced the notion of a fuzzy topology on a set X as a subset τ ⊆ [0, 1] satisfying the natural counterparts of the axioms of topology: (1) 0X , 1X ∈ τ ; (2) U, V ∈ τ ⇒ U ∧ V...

This talk aims at presenting a new way of approaching topological structures, induced by recent developments in the eld of lattice-valued topology, and deemed to incorporate in itself both crisp and many-valued settings. Based on category theory and universal algebra, the new framework is called categorically-algebraic (catalg) [9-12], to underline its motivating theories, on one hand, and to d...

This paper considers metrics valued in abelian `-groups and their induced topologies. In addition to a metric into an `-group, one needs a filter in the positive cone to determine which balls are neighborhoods of their center. As a key special case, we discuss a topology on a lattice ordered abelian group from the metric dG and the filter of positives consisting of the weak units of G; in the c...

For a Tychonoff space $X$, we denote by $C_p(X)$ the space of all real-valued continuous functions on $X$ with the topology of pointwise convergence.  We study a functional characterization of the covering property of Hurewicz.