Neometric spaces
type: Item
instance of: scholarly article
title: Neometric spaces
zbMATH Open document ID: 0854.03060
author: Sergio Fajardo
author: H. Jerome Keisler
published in: Advances in Mathematics
publication date: 1996-06-16T00:00:00Z
review text: This very long article is much too extensive for a completely detailed review. However, I do present an outline of its major features. The first section gives the basic notions that produce the neometric spaces. Next the authors apply Robinson-styled nonstandard analysis to these notions and show that nonstandard universes are a rich source of neometric families. They present a hugh neometric family that contains all previously studied neometric spaces. Further, the hugh neometric family contains rich adapted spaces, and this yields that such spaces exist. The authors also consider neometric spaces whose elements are functions from a probability space into another neometric space. Using a \(\kappa\)-saturated nonstandard universe, where \(\kappa > \omega_1\), they complete this article with a brief investigation of the stronger theory of \(\kappa\)-neometric spaces.
Mathematics Subject Classification ID: 03H05
Mathematics Subject Classification ID: 60A99
zbMATH DE Number: 889813
zbMATH Keywords: neometric spaces
zbMATH Keywords: nonstandard analysis
zbMATH Keywords: probability space
MaRDI profile type: Publication
OpenAlex ID: W4210817023
DOI: 10.1006/AIMA.1996.0020
Recommended article: Q4328568
Recommended article: Shape Spaces
Recommended article: Q5566239
Recommended article: Hyperbolic spaces
Recommended article: Q3153300
Recommended article: Holonomic Spaces
Recommended article: Q4877236
description: scientific article; zbMATH DE number 889813