**Nonstandard Analysis in Topology**

by Sergio Salbany, Todor Todorov

**Publisher**: arXiv 2011**Number of pages**: 48

**Description**:

We present Nonstandard Analysis in the framework of the superstructure of a given infinite set. We also present several applications of this axiomatic approach to point-set topology. Some of the topological topics such as the Hewitt real compactification and the nonstandard characterization of the sober spaces seem to be new in the literature on nonstandard analysis.

Download or read it online for free here:

**Download link**

(380KB, PDF)

## Similar books

**Real Variables: With Basic Metric Space Topology**

by

**Robert B. Ash**-

**Institute of Electrical & Electronics Engineering**

A text for a first course in real variables for students of engineering, physics, and economics, who need to know real analysis in order to cope with the professional literature. The subject matter is fundamental for more advanced mathematical work.

(

**58310**views)

**General Topology**

by

**Pierre Schapira**-

**Université Paris VI**

The aim of these lecture notes is to provide a short and self-contained presentation of the main concepts of general topology. Table of contents: Topological spaces; Metric spaces; Compact spaces; Banach spaces; Connectness and homotopy.

(

**6496**views)

**Metric and Topological Spaces**

by

**T. W. Körner**-

**University of Cambridge**

Contents: What is a metric?; Examples of metric spaces; Continuity and open sets for metric spaces; Closed sets for metric spaces; Topological spaces; Interior and closure; More on topological structures; Hausdorff spaces; Compactness; etc.

(

**5186**views)

**Algebraic General Topology**

by

**Victor Porton**-

**Mathematics21.org**

I introduce the concepts of funcoids which generalize proximity spaces and reloids which generalize uniform spaces. Funcoid is generalized concept of proximity, the concept of reloid is cleared from superfluous details concept of uniformity.

(

**4556**views)