The Hyperreals enlargement sets and its application on compact topology
DOI:
https://doi.org/10.37376/asj.vi6.5139Keywords:
Hyperreal numbers, infinitesimal, ultrafilter,, enlargement set, nonstandard elements, halo, compact topology.Abstract
This paper presents a study of hyperreal numbers and their relations to real numbers. The hyperreals are a number system extension of the real number system. With this system, simpler and more intuitively natural definition (topological notions of special points and compactness), proofs (Heine-Borel theorem), and new concepts (limited, unlimited numbers, enlargement sets, and halos) of mathematical interest are offered.
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