After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-ˇCech 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 elementary number theory into βN

After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-ˇCech 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 elementary number theory into βN