Geodesic
Separating Points of βN By Minimal Flows
Canadian journal of mathematics, Tome 46 (1994) no. 4, pp. 758-771

Voir la notice de l'article provenant de la source Cambridge University Press

We consider minimal left ideals L of the universal semigroup compactification of a topological semigroup S. We show that the enveloping semigroup of L is homeomorphically isomorphic to if and only if given q ≠ r in , there is some p in the smallest ideal of with qp ≠ rp. We derive several conditions, some involving minimal flows, which are equivalent to the ability to separate q and r in this fashion, and then specialize to the case that S = , and the compactification is . Included is the statement that some set A whose characteristic function is uniformly recurrent has .
DOI : 10.4153/CJM-1994-043-8
Mots-clés : 22A30 
Hindman, Neil; Lawson, Jimmie; Lisan, Amha. Separating Points of βN By Minimal Flows. Canadian journal of mathematics, Tome 46 (1994) no. 4, pp. 758-771. doi: 10.4153/CJM-1994-043-8
@article{10_4153_CJM_1994_043_8,
     author = {Hindman, Neil and Lawson, Jimmie and Lisan, Amha},
     title = {Separating {Points} of {\ensuremath{\beta}N} {By} {Minimal} {Flows}},
     journal = {Canadian journal of mathematics},
     pages = {758--771},
     year = {1994},
     volume = {46},
     number = {4},
     doi = {10.4153/CJM-1994-043-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-043-8/}
}
TY  - JOUR
AU  - Hindman, Neil
AU  - Lawson, Jimmie
AU  - Lisan, Amha
TI  - Separating Points of βN By Minimal Flows
JO  - Canadian journal of mathematics
PY  - 1994
SP  - 758
EP  - 771
VL  - 46
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-043-8/
DO  - 10.4153/CJM-1994-043-8
ID  - 10_4153_CJM_1994_043_8
ER  - 
%0 Journal Article
%A Hindman, Neil
%A Lawson, Jimmie
%A Lisan, Amha
%T Separating Points of βN By Minimal Flows
%J Canadian journal of mathematics
%D 1994
%P 758-771
%V 46
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1994-043-8/
%R 10.4153/CJM-1994-043-8
%F 10_4153_CJM_1994_043_8

[1] 1. Baker, J. and Milnes, P., The ideal structure of the Stone-Cech compactification of a group, Math. Proc. Cambridge Philos. Soc. 82(1977), 401–409. Google Scholar

[2] 2. Berglund, J. and Hindman, N., Sums of idempotents in , Semigroup Forum 44(1992), 107–111. Google Scholar

[3] 3. Berglund, J., Junghenn, H. and Milnes, P., Analysis on Semigroups, Wiley, New York, 1989. Google Scholar

[4] 4. Ellis, R., A semigroup associated with a transformation group, Trans. Amer. Math. Soc. 94( 1960), 272–281. Google Scholar

[5] 5. Ellis, R., Lectures on Topological Dynamics, Benjamin, New York, 1969. Google Scholar

[6] 6. Furstenberg, H., Recurrence in Ergodic Theory and Combinatorial Number Theory, Princeton Univ. Press, Princeton, 1981. Google Scholar

[7] 7. Gottschalk, W., Almost periodic points with respect to transformation semi-groups, Ann. of Math. 47(1946), 762–766. Google Scholar

[8] 8. Hindman, N., Minimal ideals and cancellation in , Semigroup Forum 25(1982), 291–310. Google Scholar

[9] 9. Hindman, N., Sums equal to products in , Semigroup Forum 21(1980), 221–255. Google Scholar

[10] 10. Hindman, N., Ultrafilters and combinatorial number theory. In: Number Theory Carbondale, Springer Lecture Notes in Math. (ed. M. Nathanson),751, 1979, 119–184. Google Scholar

[11] 11. Lawson, J. and A. Lisan, Transitive flows: a semigroup approach, Mathematika 38(1991), 348–361. Google Scholar

[12] 12. Ruppert, W., Compact semitopological semigroups: an intrinsic theory, Lecture Notes in Math. 1079, Springer, 1984. Google Scholar

[13] 13. Ruppert, W., Endomorphic actions of on the torus group, Semigroup Forum 43(1991), 202–217. Google Scholar

[14] 14. Strauss, D., Ideals and commutativity in , Topology Appl., to appear. Google Scholar

Cité par Sources :