In this paper, we consider an economy with infinitely many commodities and non-convex production sets. We propose a definition of the marginal pricing rule which allows us to encompass the case of smooth and convex production sets. We also show the link with the definition used in a finite dimensional setting where the marginal pricing rule is defined by means of the Clarke’s normal cone. We pr...

In this paper,  it is shown that the category of $L$-ordered fuzzifying convergence spaces contains the category of pretopological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory and the latter contains the category of topological $L$-ordered fuzzifying convergence spaces as a bireflective subcategory. Also, it is proved that the category of $L$-ordered fuzzifying conver...

In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievableexample is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for thebasis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroidis equivalent to a mapping which satisfies the basis ...

In this paper, some characterizations of fuzzifying strong compactness are given, including in terms nets and presubbases. Several locally the framework topology introduced mapping theorems obtained.

Some fixed point theorems and common fixed point theorem in Logarithmic convex structure areproved.

In this article we research the structure of d-convex simple graphs in order to extend the already known classes of graphs of this type. We do this using some new operations and new graphs. We introduce the notion of M-prime graphs and split all d-convex simple graphs into M-prime graphs using the M operation. After that we describe all M-prime graphs we know. Mathematics subject classification...

Given an o-minimal structure M with a group operation, we show that for a properly convex subset U , the theory of the expanded structure M′ = (M, U) has definable Skolem functions precisely when M′ is valuational. As a corollary, we get an elementary proof that the theory of any such M′ does not satisfy definable choice. §