Neometric spaces
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.
scientific article; zbMATH DE number 889813