Nonstandard Analysis in Topology

2011/07/17 by Sergio Salbany, Salbany, Sergio, Todor Todorov +1
Mathematics · #03H05 #54D10 #54D15 #54D30 #54D35 #54D60 #54J05 #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Mathematical and Theoretical Analysis #Rings, Modules, and Algebras #math.GN #msc:03H05 #msc:54D10 #msc:54D15 #msc:54D30 #msc:54D35 #msc:54D60 #msc:54J05

paper · pdf · doi:10.48550/arxiv.1107.3323

48 pages

arxiv created 2011/07/17 · openalex publication_date 2011/07/17 · arxiv updated 2011/07/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present Nonstandard Analysis by three axioms: the \em Extension, Transfer and Saturation Principles 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 realcompactification and the nonstandard characterization of the sober spaces seem to be new in the literature on nonstandard analysis. Others have already close counterparts but they are presented here with essential simplifications.

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