Topological properties of some algebraically defined subsets of βN
| Autor: | Neil Hindman, Dona Strauss |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Semigroup
010102 general mathematics Multiplicative function Mathematics::General Topology Topological semigroup 0102 computer and information sciences Topology 01 natural sciences 010201 computation theory & mathematics Countable set Geometry and Topology Topological group Compactification (mathematics) 0101 mathematics Mathematics |
| Zdroj: | Topology and its Applications. 220:43-49 |
| ISSN: | 0166-8641 |
| DOI: | 10.1016/j.topol.2017.02.001 |
| Popis: | Let S be a discrete semigroup and let the Stone–Cech compactification βS of S have the operation extending that of S which makes βS a right topological semigroup with S contained in its topological center. We show that the closure of the set of multiplicative idempotents in β N does not meet the set of additive idempotents in β N . We also show that the following algebraically defined subsets of β N are not Borel: the set of idempotents; the smallest ideal; any semiprincipal right ideal of N ⁎ ; the set of idempotents in any left ideal; and N ⁎ + N ⁎ . We extend these results to βS, where S is an infinite countable semigroup algebraically embeddable in a compact topological group. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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