Nonstandard analysis: Its creator and place

- Algebras and Nonstandard Analysis

Suppose B is an ultraproduct of finite dimensional C∗-algebras. We consider mapping and injectability properties for separable C∗algebras into B. In the case of approximately finite C∗-algebras, we obtain a classification of these mappings up to inner conjugacy. Using a Theorem of Voiculescu, we show that for nuclear C ∗-algebras injectability into an ultraproduct of finite dimensional C ∗-alge...

Nonstandard Analysis in Topology: Nonstandard and Standard Compactifications

Let (X,T ) be a topological space, and X a non–standard extension of X . There is a natural “standard” topology T on X generated by G, where G ∈ T . The topological space ( X, T ) will be used to study, in a systematic way, compactifications of (X,T ) . Mathematics Subject Classification: 031105, 54J05, 54D35, 54D60.

Nonstandard Analysis and Generalized Functions

This application of nonstandard analysis utilizes the notion of the highly-saturated enlargement. These nonstandard methods are applied to the theory of generalized functions (distributions) and demonstrates how such analysis clarifies many aspects of this theory. 1. Additional Modeling Concepts. In what follows, the basic notation and definitions are as they appear in [3]. However, except as m...

Unifying Constructive and Nonstandard Analysis

Nonstandard Analysis in Point

We present Nonstandard Analysis by three axioms: the Extension, Transfer and Saturation Principles in the framework of the superstructure of a given innnite set. We also present several applications of this axiomatic approach to point-set topology. Some of the topological topics such as the Hewitt realcompactiication and the nonstandard characterization of the sober spaces seem to be new in the...