A ‘‘metric” characterization of reflexivity

A Characterization of Reflexivity

We give a characterization of reflexivity in terms of rotundity of the norm. Renorming characterization of various classes of Banach spaces is important and useful for applications. Some classes turn out to have very elegant descriptions, while most seem to resist the renorming point of view. The most spectacular result in this area is certainly the Enflo-Pisier characterization of superreflexi...

Demand Functions and a Characterization of Reflexivity

We show that in reflexive Banach spaces there are two classes of closed cones (consumption sets) i.e. cones whose any budget set is bounded and cones whose any budget set is unbounded. We prove that in the first category of these cones the demand correspondence of any upper semicontinuous preference relation exists and we show also that this property characterizes the reflexive spaces. Moreover...

A Geometrical Characterization of Reflexivity in Banach Spaces

A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION

‎The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$‎. ‎In this case‎, ‎$B$ is called a textit{metric basis} for $G$‎. ‎The textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$‎. ‎Givi...

A Metric Characterization of Normed Linear Spaces

Let X be a linear space over a field K = R or C, equipped with a metric ρ. It is proved that ρ is induced by a norm provided it is translation invariant, real scalar “separately” continuous, such that every 1-dimensional subspace of X is isometric to K in its natural metric, and (in the complex case) ρ(x, y) = ρ(ix, iy) for any x, y ∈ X.