Divisibility in the Stone-Čech compactification
Divisibility in the Stone-Čech compactification
Author(s): Boris ŠobotSubject(s): Philosophy, Logic
Published by: Wydawnictwo Uniwersytetu Jagiellońskiego
Summary/Abstract: After defining continuous extensions of binaryrelations on the set N of natural numbers to its Stone-ˇCech ompactification βN, we establish some results about one of suchextensions. This provides us with one possible divisibility relationon βN,, and we introduce a few more, defined in a naturalway. For some of them we find equivalent conditions for divisibility.Finally, we mention a few facts about prime and irreducibleelements of (βN, ·). The motivation behind all this is to try totranslate problems in elementary number theory into βN.
Journal: Reports on Mathematical Logic
- Issue Year: 2015
- Issue No: 50
- Page Range: 53-66
- Page Count: 14
- Language: English