English

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.

Keywords

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}
}
R2 v1 2026-06-22T06:35:45.732Z