Divisibility in the Stone-\v{C}ech compactification
General Topology
2014-10-27 v1
Abstract
After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Cech compactification \beta N, we establish some results about one of such extensions. This provides us with one possible divisibility relation on \beta N and we introduce a few more, defined in a natural way. For some of them we find equivalent conditions for divisibility. Finally, we mention a few facts about prime and irreducible elements of (\beta N, \cdot). The motivation behind all this is to try to translate problems in number theory into \beta N.
Cite
@article{arxiv.1410.6778,
title = {Divisibility in the Stone-\v{C}ech compactification},
author = {Boris Šobot},
journal= {arXiv preprint arXiv:1410.6778},
year = {2014}
}