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Nonstandard Analysis in Topology

book
Language:
Author: Sergio Salbany and Todor Todorov
Url: http://arxiv.org/pdf/1107.3323v1
Format: Pdf
Year: 2011
Category: Analysis
Pages: 48
Clicks: 1315

Description
We present Nonstandard Analysis by three axioms: the Extension, Transfer and Saturation Principles in the framework of the superstruc- ture 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 characteri- zation 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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