A characterization of locally euclidean spaces

A Characterization of Locally Euclidean Spaces

Locally Peripherally Euclidean Spaces Are Locally Euclidean, Ii.

A Characterization of Euclidean Spaces

The purpose of this paper is to give an elementary proof of the fact that a Banach space in which there exist projection transformations of norm one on every two-dimensional linear subspace is a euclidean space. S. Kakutani [ l ] has pointed out that a modification of a proof due to Blaschke [2] will prove this theorem. F. Bohnenblust has been able to establish this theorem for the complex case...

A Metric Characterization of Snowflakes of Euclidean Spaces

We give a metric characterization of snowflakes of Euclidean spaces. Namely, a metric space is isometric to Rn equipped with a distance (dE) , for some n ∈ N0 and ∈ (0, 1], where dE is the Euclidean distance, if and only if it is locally compact, 2-point isometrically homogeneous, and admits dilations of any factor.

A Characterization of Certain Conformally Euclidean Spaces of Class One

1. In this paper we will examine the metrics of conformally Euclidean spaces Cn (n^A) having the following two properties: (1) They are locally and isometrically imbeddable in Euclidean space of one higher dimension (£n+i), i.e. they are of class one. (2) With respect to a conformai coordinate system, the matrix of the second fundamental tensor [èy] has diagonal form. The condition for class on...