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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Disjointness in transformation groups


Author: Harvey B. Keynes
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
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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.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0397687-1
Keywords: Minimal transformation group, disjointness, bitransformation group, distal extensions, proximal extensions
Article copyright: © Copyright 1972 American Mathematical Society