In this paper, we study the category of quantale-valued preordered spaces. We show that it is a normalized topological and give characterization zero-dimensionality D-connectedness in Moreover, characterize explicitly each T0, T1, pre-T2, T2 NT2 Finally, examine how these are related to other full subcategory Ti(pre-T2(L-Prord)) (i=0,1,2) pre-T2(L-Prord), Ti (L-Prord) (i=1,2) L-Prord isomorphic.

The paper provides a quantitative algebraic analysis of a BB’84-type quantum key distribution protocol. The analysis is done in an algebraic setting, where classical and quantum variables form a module for the quantale formed from the communication and quantum actions. The module-quantale pair is endowed with sup-maps that encode uncertainties of agents involved in the protocol, about the varia...

The reticulation of an algebra was first defined for commutative rings by Simmons [19] and it was extended by Belluce to non-commutative rings [3]. As for the algebras of fuzzy logics, Belluce also constructed the reticulation of an MV-algebra [2], G. Georgescu defined the reticulation of a quantale [8] and L. Leuştean made this construction for BL-algebras [13, 14]. In each of the papers cited...

In previous papers, several $T_{0}$ and Hausdorff objects in topological categories are introduced compared. The main objectives of this paper to characterize $\overline{T_{0}}$, $T_{0}$, $T_{1}$ pre-$\overline{T_{2}}$ the category quantale-valued closure space as well examine their mutual relationship.

We propose various methods for combining or amalgamating propositional languages and deductive systems. make heavy use of quantales quantale modules in the wake previous works by present other authors. also describe quite extensively relationships among algebraic order-theoretic constructions corresponding ones based on a purely logical approach.

When replacing the non-negative real numbers with their addition by a commutative quantale V, under a metric lens one may then view small V-categories as sets that come with a V-valued distance function. The ensuing category V-Cat is well known to be a concrete topological category that is symmetric monoidal closed. In this paper we show which concrete symmetric monoidalclosed topological categ...

The characterization of stably closed maps of topological spaces as the closed maps with compact fibres and the role of the Kuratowski-Mrówka’ Theorem in this characterization are being explored in the general context of lax (T, V )-algebras, for a quantale V and a Setmonad T with a lax extension to V -relations. The general results are being applied in standard (topological and metric) and non...

We define the Lukasiewicz Transform as a residuated map and a homomorphism between semimodules over the semiring reducts of an MV-algebra. Then we describe the “ Lukasiewicz Transform Based” ( LTB) algorithm for image processing. We also propose a strong extension of such concepts and results in the framework of quantales and quantale modules. 1 The Lukasiewicz transform and its applications Th...