Vol. 104, No. 2, 1983

Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Homomorphisms of minimal flows and generalizations of weak mixing

Douglas C. McMahon and Ta-Sun Wu

Vol. 104 (1983), No. 2, 401–416
Abstract

In this paper we are concerned with generalizations of weakly mixing. Let ϕ : (X,T) (Y,T) be a homomorphism of metric minimal flows and let S(ϕ) denote the relativized equicontinuous structure relation. The main result is that if ϕ has a RIM, λ, and z Z such that the support of λz equals the fiber X0 = ϕ1(z), then:

oc(V1 × ⋅⋅⋅Vn ) ⊇ S(ϕ)(V1) × ⋅⋅⋅× S(ϕ)(Vn),

and also there exists a dense set of points x1,x2,x3, in X0 such that oc(x1,x2,x3,) S(ϕ)(x1) × S(ϕ)(x2) × .

Mathematical Subject Classification 2000
Primary: 54H20
Milestones
Received: 9 April 1981
Published: 1 February 1983
Authors
Douglas C. McMahon
Ta-Sun Wu