Related papers: Rough $I$-convergence in cone metric spaces
The theory of convergent graph sequences has been worked out in two extreme cases, dense graphs and bounded degree graphs. One can define convergence in terms of counting homomorphisms from fixed graphs into members of the sequence…
Suppose that a sequence of metric measure spaces X_n=(X_n, d_n, m_n) satisfies RCD*(K,N) with Diam(X_n) <D and m_n(X_n)=1. Then Sturm's D-convergence of X_n is equivalent to the weak convergence of the laws of Brownian motions on X_n.
We prove convergence rates of explicit finite difference schemes for the linear advection and wave equation in one space dimension with H\"older continuous coefficient. The obtained convergence rates explicitly depend on the H\"older…
The paper deals with pretangent spaces to general metric spaces. An ltrametricity criterion for pretangent spaces is found and it is closely related to the metric betweenness in the pretangent spaces.
The problem of defining correctly geometric objects such as the curvature is a hard one in discrete geometry. In 2009, Ollivier defined a notion of curvature applicable to a wide category of measured metric spaces, in particular to graphs.…
We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning…
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…
We provide sufficient conditions for norm convergence of various projection and reflection methods, as well as giving limiting examples regarding convergence rates.
We show that the the image of the regular projection of a vertex of a cone over a triangle that minimizes the ratio of the cube of the area of the boundary of the cone and the square of the volume of the cone coincides with the incenter.
We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Buesemann, our concept also applies to metric spaces that might…
In this paper, we investigate the properties of sequences and series under the action of the log-concave operator \(\mathcal{L}\). We explore the relationship between the convergence of a sequence \((a_k)\) and the convergence of sequences…
We say that an ideal I is homogeneous, if its restriction to any I-positive subset is isomorphic to I. The paper investigates basic properties of this notion -- we give examples of homogeneous ideals and present some applications to…
Weak convergence of probability measures is one of the most important topics in the field probability and statistics. In this survey paper, we look at weak convergence of probability measures from the topological vector space point of view.…
An effective radius of convergence is defined and computed for any truncated Taylor series. Applications to well known series are performed and is shown that a range of good coincidence for actual and approximative plot can always be found.…
The influence of errors on the convergence of infinite products of weak quasi-contraction mappings in $b$-metric spaces is explored. An example demonstrating the necessity of convergence of the sequence of computational errors to zero is…
Connections between continuous and discrete worlds tend to be elusive. One example is curvature. Even though there exist numerous nonequivalent definitions of graph curvature, none is known to converge in any limit to any traditional…
Rough sets are approximations of concrete sets. The theory of rough sets has been used widely for data-mining. While it is well-known that adjunctions are underlying in rough approximations, such adjunctions are not enough for…
Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of $X$ that is a strong deformation retract. We provide a…
This paper deals with three major types of convergence of probability measures on metric spaces: weak convergence, setwise converges, and convergence in the total variation. First, it describes and compares necessary and sufficient…
In this paper we introduce the concept of the rectangular metric like spaces, along with its topology and we prove some fixed point theorems under different contraction principles. We introduce the concept of modified metric-like space as…