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The Semigroup of Ultrafilters Near 0.
- Source :
-
Semigroup Forum . 1999, Vol. 59 Issue 1, p33. 23p. - Publication Year :
- 1999
-
Abstract
- The set 0+ of ultrafilters on (0,1) that converge to 0 is a semigroup under the restriction of the usual operation + on &BetaR[subd] the Stone-Çech compactification of the discrete semigroup (R[subd], +). It is also a subsemigroup of Β((0, 1)[subd]). The interaction of these operations has recently yielded some strong results in Ramsey Theory. Since (0[sup+],.) is an ideal of &Beta((0, 1)[subd],.), much is known about the structure of (0[sup+],.). On the other hand, (0[sup+],+) is far from being an ideal of (ΒR[subd],+) so little about its algebraic structure follows from known results. We characterize here the smallest ideal of (0[sup+],+), its closure, and those sets "central" in (0[sup+],+), that is, those sets which are members of minimal idempotents in (0[sup+],+). We derive new combinatorial applications of those sets that are central in (0[sup+],+). [ABSTRACT FROM AUTHOR]
- Subjects :
- *SEMIGROUPS (Algebra)
*ULTRAFILTERS (Mathematics)
*RAMSEY theory
*IDEMPOTENTS
Subjects
Details
- Language :
- English
- ISSN :
- 00371912
- Volume :
- 59
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Semigroup Forum
- Publication Type :
- Academic Journal
- Accession number :
- 8856740
- Full Text :
- https://doi.org/10.1007/s002339900031