相关论文: The convergence space of minimal usco mappings

Power-law uniform (in the operator norm) convergence on vector subspaces with their own norms in von Neumann's ergodic theorem with continuous time is considered. All possible exponents of the considered power-law convergence are found; for…

Consider $d$ disjoint closed subintervals of the unit interval and consider an orientation preserving expanding map which maps each of these subintervals to the whole unit interval. The set of points where all iterates of this expanding map…

In this paper we give a unitary approach for the simultaneous study of the convergence of discrete and integral operators described by means of a family of linear continuous functionals acting on functions defined on locally compact…

We discuss five simple functions on finite multisets of metric spaces. The first four are all metrics iff the underlying space is bounded and are complete metrics iff it is also complete. Two of them, and the fifth function, all generalise…

A translation structure on a surface is an atlas of charts to the plane so that the transition functions are translations. We allow our surfaces to be non-compact and infinite genus. We endow the space of all pointed surfaces equipped with…

There have been many parallel streams of research studying order isomorphisms of some specific sets $G$ of functions from a set $X$ to $\mathbb{R}\cup\{\pm\infty\}$, such as the sets of convex or Lipschitz functions. We develop in this…

We study the class of compact convex subsets of a topological vector space which admits a strictly convex and lower semicontinuous function. We prove that such a compact set is embeddable in a strictly convex dual Banach space endowed with…

In aperiodic order, non-periodic but "ordered" objects such as tilings, Delone sets, functions and measures are investigated. In this article we depict the common structure of these objects by using the general framework of abstract pattern…

Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on arying spaces is natural. However, it seems that the first…

This is an intuitive survey of extrinsic and intrinsic notions of convergence of manifolds complete with pictures of key examples and a discussion of the properties associated with each notion. We begin with a description of three extrinsic…

Condensed mathematics, developed by Clausen and Scholze over the last few years, proposes a generalization of topology with better categorical properties. It replaces the concept of a topological space by that of a condensed set, which can…

This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff…

Given a point and an expanding map on the unit interval, we consider the set of points for which the forward orbit under this map is bounded away from the given point. For maps like multiplication by an integer modulo 1, such sets have full…

Shimizu and Takahashi have shown that every decreasing sequence of nonempty, bounded, closed, convex subsets of a complete, uniformly Takahashi convex metric space has nonempty intersection. It is well known that the Menger convexity is a…

Optimization problems, generalized equations, and the multitude of other variational problems invariably lead to the analysis of sets and set-valued mappings as well as their approximations. We review the central concept of set-convergence…

We announce and examine the conjecture that each infinite connected normal Hausdorff space has a quotient homeomorphic to the unit interval, shown to be true with the additional assumption of compactness or local connectedness. Some…

We discuss here geometric structures of condensed matters by means of a fundamental topological method. Any geometric pattern can be universally represented by a decomposition space of a topological space consisting of the infinite product…

The classical Hausdorff dimension of finite or countable sets is zero. We define an analog for finite sets, called finite Hausdorff dimension which is non-trivial. It turns out that a finite bound for the finite Hausdorff dimension…

We prove that a region in a two-dimensional affine subspace of a normed space $V$ has the least 2-dimensional Hausdorff measure among all compact surfaces with the same boundary. Furthermore, the 2-dimensional Hausdorff area density admits…

In these notes, uniform convergence on compacta is studied on the space of functions taking values in the set of finite Borel measures. Related limit theorems, including L\'evy's continuity theorem and functional limit theorems for…