lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...

let g = (v,e) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. in this paper, we associate a topology to g, called graphic topology of g and we show that it is an alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. then we investigate some properties of this topology. our motivation is to give an e...

We study the relationship between two stratifications on parameter spaces for coherent sheaves and for quiver representations: a stratification by Harder–Narasimhan types and a stratification arising from the geometric invariant theory construction of the associated moduli spaces of semistable objects. For quiver representations, both stratifications coincide, but this is not quite true for she...

In this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. It gives some criterions to study locally convex topological spaces in a discrete approach.

We give a full description of all the canonical algebras over an algebraically closed field that are derived equivalent to incidence algebras of finite posets. These are the canonical algebras of weight type other than (1, p) whose number of weights does not exceed 3. This note concerns the characterization of the canonical algebras over an algebraically closed field that are derived equivalent...

H(X,C) = ⊕p+q=kH (X). A class α ∈ H(X,Q) is said to be a rational Hodge class if its image in H(X,C) belongs to H(X). As is well known, the classes which are Poincaré dual to irreducible algebraic subvarieties of codimension p of X are degree 2p Hodge classes. The Hodge conjecture asserts that any rational Hodge class is a combination with rational coefficients of such classes. In the case of a...