2014/10/24 by Boris Šobot, Šobot, Boris
Computer Science · Mathematics · #22A15 #54D35 #54D80 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #General Topology (math.GN) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.1410.6778
openalex publication_date 2014/10/24 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28
After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Cech compactification βN, we establish some results about one of such extensions. This provides us with one possible divisibility relation on βN 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 (βN, ⋅). The motivation behind all this is to try to translate problems in number theory into βN.