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Divisibility in the Stone-Čech compactification

Šobot B.

Reports on Mathematical Logic

2015

Vol. 50

53--66

After defining continuous extensions of binary relations on the set N of natural numbers to its Stone-Čech 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.