相关论文: Baire-one mappings contained in a usco map

We consider infinite graphs and the associated energy forms. We show that a graph is canonically compactifiable (i.e. all functions of finite energy are bounded) if and only if the underlying set is totally bounded with respect to any…

We investigate strongly separately continuous functions on a product of topological spaces and prove that if $X$ is a countable product of real lines, then there exists a strongly separately continuous function $f:X\to\mathbb R$ which is…

We present several characterizations of uo-convergent nets or sequences in spaces of continuous functions $C(\Omega)$, $C_b(\Omega)$, $C_0(\Omega)$, and $C^\infty(\Omega)$, extending results of [vdW18]. In particular, it is shown that a…

We investigate the possibility of extension of fragmented functions from Lindel\"{o}f subspaces of completely regular spaces and find necessary and sufficient conditions on a fragmented Baire-one function to be extendable on any completely…

We say that a metric graph is uniformly bounded if the degrees of all vertices are uniformly bounded and the lengths of edges are pinched between two positive constants; a metric space is approximable by a uniform graph if there is one…

Given $n$ distinct points $\mathbf{x}_1, \ldots, \mathbf{x}_n$ in $\mathbb{R}^d$, let $K$ denote their convex hull, which we assume to be $d$-dimensional, and $B = \partial K $ its $(d-1)$-dimensional boundary. We construct an explicit…

The paper considers the spaces $B_p[1, \alpha]$ of all Baire functions $x\colon [1,\alpha]\to \mathbb{R}$, defined on segments of ordinals $[1,\alpha]$ and endowed with the topology of pointwise convergence. A complete topological…

In this paper, we propose criteria for unboundedness of the images of set-valued mappings having closed graphs in Euclidean spaces. We focus on mappings whose domains are non-closed or whose values are connected. These criteria allow us to…

Consider a set of continuous maps from the interval $[0,1]$ to a domain in ${\mathbb R}^d$. Although the topological boundary of this set in the path space is not smooth in general, by using the theory of functions of bounded variation (BV…

Many concrete problems are formulated in terms of a finite set of points in $R^n$ which, via the ambient Euclidean metric, becomes a finite metric space. To obtain information from such a space, it is often useful to associate a graph to…

This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…

In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…

Piecewise smooth systems are intensively studied today in many application areas, such as economics, finance, engineering, biology, and ecology. In this work, we consider a class of one-dimensional piecewise linear discontinuous maps with a…

We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…

In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.

A topological space $X$ is Baire if the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems for the space of Baire functions is the Banakh-Gabriyelyan problem: Let $\alpha$ be a…

We investigate classes of functions from a topological space to a metric space that are related to those of Borel class 1. Following the idea defining an equi-Baire 1 family (due to Lecomte) we define the respective equi-families of…

We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.

We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.

We consider discrete metric spaces and we look for non-constant contractions. We introduce the notion of contractive map and we characterize the spaces with non-constant contractive maps. We provide some examples to discussion the possible…