Disjointness in transformation groups
HTML articles powered by AMS MathViewer
- by Harvey B. Keynes PDF
- Proc. Amer. Math. Soc. 36 (1972), 253-259 Request permission
Abstract:
In this paper, we shall be concerned with the question of what conditions on minimal transformation groups will guarantee that they are disjoint. Generalizing a result of I. Bronšteĭn about lifting of minimality through group extensions to associated bitransformation groups, we prove that in a large class of transformation groups, disjointness is equivalent to disjointness of their maximal equicontinuous factors. In the abelian case, this means that disjointness is equivalent to no common factor in the class of flows discussed.References
-
I. Bronšteǐn, On distal minimal sets, Mat. Issled. 5 (1970). (Russian)
- Robert Ellis, Lectures on topological dynamics, W. A. Benjamin, Inc., New York, 1969. MR 0267561
- Robert Ellis and Harvey Keynes, A characterization of the equicontinuous structure relation, Trans. Amer. Math. Soc. 161 (1971), 171–183. MR 282357, DOI 10.1090/S0002-9947-1971-0282357-4
- Harvey B. Keynes, The structure of weakly mixing minimal transformation groups, Illinois J. Math. 15 (1971), 475–489. MR 286090
- Reuven Peleg, Weak disjointness of transformation groups, Proc. Amer. Math. Soc. 33 (1972), 165–170. MR 298642, DOI 10.1090/S0002-9939-1972-0298642-2
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 253-259
- MSC: Primary 54H15; Secondary 54H20
- DOI: https://doi.org/10.1090/S0002-9939-1972-0397687-1
- MathSciNet review: 0397687