Divisibility in the Stone-Cech compactification
Abstract
After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Cech compactification β N, we establish some results about one of such extensions. This provides us with one possible divisibility relation on β 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 (β N, ·). The motivation behind all this is to try to translate problems in number theory into β N.
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