The term Stone-type duality often refers to a dual equivalence between category of lattices or other partially ordered structures on one side and topological the other. This paper is part larger endeavour that aims extend web dualities from metric and, more generally, quantale-enriched categories. In particular, we improve our previous work show how certain results for categories [ 0 , 1 ] -enr...

Vaughan Pratt has introduced objects consisting of pairs (A, W ) where A is a set and W a set of subsets of A, such that (i) W contains ∅ and A, (ii) if C is a subset of A×A such that for every a ∈ A, both {b | (a, b) ∈ C} and {b | (b, a) ∈ C} are members of W (a “crossword” with all “rows” and “columns” in W ), then {b | (b, b) ∈ C} (the “diagonal word”) also belongs to W, and (iii) for all di...

Our work over the past years shows that not only the collection of (for instance) all topological spaces gives rise to a category, but also each topological space can be seen individually as a category by interpreting the convergence relation x −→ x between ultrafilters and points of a topological space X as arrows in X. Naturally, this point of view opens the door to the use of concepts and id...

ELECTRE TRI-nB is a method designed to sort alternatives evaluated on several attributes into ordered categories. It an extension of TRI-B that uses limiting profiles, instead one, delimit each category. In previous paper we have characterized the partitions can be obtained with TRI-nB, using simple axiom called linearity. The simplicity this characterization crucially rests possibility use as ...

The organization of human lateral occipitotemporal cortex (lOTC) has been characterized largely according to two distinct principles: retinotopy and category-selectivity. Whereas category-selective regions were originally thought to exist beyond retinotopic maps, recent evidence highlights overlap. Here, we combined detailed mapping of retinotopy, using population receptive fields (pRF), and ca...

Electre Tri is a set of methods designed to sort alternatives evaluated on several criteria into ordered categories. In these methods, are assigned categories by comparing them with reference profiles that represent either the boundary or central elements category. The original Tri-B method uses one limiting profile for separating category from below. A more recent method, Tri-nB, allows use sa...

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

We consider the minimization problem f (x) → min, x ∈ K , where K is a closed subset of an ordered Banach space X and f belongs to a space of increasing lower semicontinuous functions on K . In our previous work, we showed that the complement of the set of all functions f , for which the corresponding minimization problem has a solution, is of the first category. In the present paper we show th...

It is well known that the internal suplattices in the topos of sheaves on a locale are precisely the modules on that locale. Using enriched category theory and a lemma on KZ doctrines we prove (the generalization of) this fact in the case of ordered sheaves on a small quantaloid. Comparing module-equivalence with sheaf-equivalence for quantaloids and using the notion of centre of a quantaloid, ...

in this paper, we introduce the concept of semihyperring $(r,+,cdot)$ together with a suitable partial order $le$. moreover, we introduce and study hyperideals in ordered semihyperrings. simple ordered semihyperrings are defined and its characterizations are obtained. finally, we study some properties of quasi-simple and $b$-simple ordered semihyperrings.