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arXiv · 1410.6778

Divisibility in the Stone-\v{C}ech compactification

Boris Šobot
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Abstract

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

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Boris Šobot. 2014-10-24. Divisibility in the Stone-\v{C}ech compactification. https://arxiv.org/abs/1410.6778

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