Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Finite extensions of minimal transformation groups


Authors: Robert J. Sacker and George R. Sell
Journal: Trans. Amer. Math. Soc. 190 (1974), 325-334
MSC: Primary 54H20
DOI: https://doi.org/10.1090/S0002-9947-1974-0350715-8
MathSciNet review: 0350715
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we shall study homomorphisms $ p:W \to Y$ on minimal transformation groups. We shall prove, in the case that W and Y are metrizable, that W is a finite (N-to-1) extension of Y if and only if W is an N-fold covering space of Y and p is a covering map. This result places no further restrictions on the acting group. We shall then use this characterization to investigate the question of lifting an equicontinuous structure from Y to W. We show that, under very weak restrictions on the acting group, this lifting is always possible when W is a finite extension of Y.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 54H20

Retrieve articles in all journals with MSC: 54H20


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1974-0350715-8
Keywords: Transformation groups, finite extensions, covering space, equicontinuity, distal
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society