613. Closed Euclidean Spaces

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...

Berkovich Spaces Embed in Euclidean Spaces

Let K be a eld that is complete with respect to a nonarchimedean absolute value such that K has a countable dense subset. We prove that the Berkovich analyti cation V an of any d-dimensional quasi-projective scheme V over K embeds in R. If, moreover, the value group of K is dense in R>0 and V is a curve, then we describe the homeomorphism type of V an by using the theory of local dendrites.

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...

On quasiplanes in Euclidean spaces

A variational inequality for the images of k-dimensional hyper-planes under quasiconformal maps of the n-dimensional Euclidean space is proved when 1 ≤ k ≤ n − 2 .

Equiangular lines in Euclidean spaces