Fehrele's principle in nonstandard topology

TL;DR

This paper explores Fehrele's principle in nonstandard topology, using it to prove classical theorems like Moore-Osgood and Dini's, with some generalizations, highlighting its utility in topological analysis.

Contribution

It introduces applications of Fehrele's principle to prove and generalize key theorems in topology within a nonstandard analysis framework.

Findings

Fehrele's principle characterizes internal sets in nonstandard topology.

Generalizations of Moore-Osgood and Dini's theorems are established.

The principle provides a new approach to classical topological results.

Abstract

In nonstandard analysis, Fehrele's principle is a beautiful criterion for a set to be internal, stating that every galactic halic set is internal. In this note, we use this principle to prove some well-known results in topology, including slight generalisations of the Moore-Osgood theorem and Dini's theorem.