A neometric survey

This chapter presents a new method for existence proofs, based on the concept of a neometric space. It discusses definitions and results from several other papers, and aims to explain how the ideas from these papers fit together as a whole. The neometric method is intended to be more than a proof technique— it has the potential to suggest new conjectures and new proofs in a wide variety of settings. The main point of the neometric method is that our Approximation Theorem goes beyond the familiar case of convergence in a compact set. The huge neometric family is constructed by giving an explicit definition of basic and neocompact sets that captures the way internal sets are used in nonstandard probability practice. The huge neometric family is a generalization of the approach to neocompactness originally developed in. The neometric family over a rich B-adapted space was introduced in a nonstandard setting.