Nešetřil and Ossona de Mendez introduced the notion of first order convergence, which unifies the notions of convergence for sparse and dense graphs. They asked whether if (Gi)i∈N is a sequence of graphs with M being their first order limit and v is a vertex of M , then there exists a sequence (vi)i∈N of vertices such that the graphs Gi rooted at vi converge to M rooted at v. We show that this ...

The model theory based notion of the first order convergence unifies the notions of the left-convergence for dense structures and the BenjaminiSchramm convergence for sparse structures. It is known that every first order convergent sequence of graphs with bounded tree-depth can be represented by an analytic limit object called a limit modeling. We establish the matroid counterpart of this resul...

The statistical unbounded topological convergence was studied and investigated with respect to the solid topology in locally Riesz spaces. In this paper, we introduce order spaces by developing a topology-free technique on Moreover, give some relations other kinds of convergences.