Connectedness related to almost periodicity of compositions of flow homomorphisms

Douglas C. McMahon, Jaap C. S. P. van der Woude and Ta-Sun Wu

Vol. 128 (1987), No. 1, 127–148

DOI: 10.2140/pjm.1987.128.127

Abstract

Consider homomorphisms ϕ : X → Y and ψ : Y → Z, where ϕ is open and N-to-one, ψ is almost periodic. In the paper by R. J Sacker and G. R. Sell, it was shown that, under a certain condition on the phase group, the composition ψ ∘ϕ : X → Z is almost periodic (provided that Z is trivial and X is minimal). In this paper almost periodicity of ψ ∘ ϕ is studied under connectedness conditions on the fibers of ψ. For instance it is shown that if ψ is almost periodic with connected fibers than ψ ⋅ ϕ is almost periodic. If ψ is locally almost periodic with locally connected fibers then ϕ ∘ ψ is locally almost periodic.

Mathematical Subject Classification 2000

Primary: 54H20

Secondary: 58F25

Milestones

Received: 12 March 1985

Revised: 31 July 1986

Published: 1 May 1987