We present some lifting theorems for continuous order-preserving functions on locally and σ-compact Hausdorff preordered topological spaces. In particular, we show that a preorder space has multi-utility representation if, only every compact subspace, function can be lifted to the entire space. Such characterization is also presented by introducing property of ≾-C-compatible closed subspaces. T...

We present some sufficient conditions for the existence of a continuous multi-utility representation of a preorder on a topological space (X, τ) (i.e., for the existence of a family F of continuous increasing realvalued functions on the preordered topological space (X, τ, ) such that, for every pair of elements (x, y) ∈ X×X, x y ⇔ f(x) ≤ f(y) ∀f ∈ F). Such conditions are based on the concept of...

In this note the authors correct and extend results presented in their article “The Isomorphism problem for incidence rings”, Pacific J. Math., 187(2) (1999), 201-214. Specifically, it is shown that for a large class of rings (including those with finite right Goldie dimension, semilocal, and many commutative rings), if P and P ′ are finite preordered sets for which there is an isomorphism of i...

An L-fuzzy context is a triple consisting of a set of objects, a set of attributes and an L-fuzzy binary relation between them. An l-cut is a classical context over the same sets with relation as a set of all object attribute pairs, which fuzzy relation assigns truth degree geater or equal than l. Proto-fuzzy concept is a triple made of a set of objects and a set of attributes, which form a con...

In this article the notion of quasi left factorization structure in a category X is given. It is proved that quasi left factorization structures correspond to subobjects of a predefined object in the category of laxed preordered valued presheaves, Lax(PrOrdX op ). The main result proves this correspondence is one to one when quasi left factorization structures are restricted to the so called QL...