Divisibility in the Stone-Čech compactification

Boris Šobot


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

Słowa kluczowe: divisibility, Stone-ˇCech compactification, ultrafilter
[1] N. Hindman, D. Strauss, Algebra in the Stone-ˇCech compactification, theory and applications. 2nd revised and extended edition, De Gruyter, 2012.

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Pierwotną formą czasopisma jest wersja elektroniczna.