Characterizations of Metric-Dependent Dimension Functions

The metric dimension and girth of graphs

A set $Wsubseteq V(G)$ is called a resolving set for $G$, if for each two distinct vertices $u,vin V(G)$ there exists $win W$ such that $d(u,w)neq d(v,w)$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The minimum cardinality of a resolving set for $G$ is called the metric dimension of $G$, and denoted by $dim(G)$. In this paper, it is proved that in a connected graph $...

On characterizations of weakly $e$-irresolute functions

The aim of this paper is to introduce and obtain some characterizations of weakly $e$-irresolute functions by means of $e$-open sets defined by Ekici [6]. Also, we look into further properties relationships between weak $e$-irresoluteness and separation axioms and completely $e$-closed graphs.

Metric Pseudoentropy: Characterizations and Applications

Metric entropy is a computational variant of entropy, often used as a convenient substitute of HILL Entropy, slightly stronger and standard notion for entropy in cryptographic applications. In this paper we develop a general method to characterize metric-type computational variants of entropy, in a way depending only on properties of a chosen class of test functions (adversaries). As a conseque...

Characterizations of Compactness for Metric Spaces

Characterizations of Sobolev Inequalities on Metric Spaces

We present isocapacitary characterizations of Sobolev inequalities in very general metric measure spaces.