TY - JOUR
T1 - Connectedness related to almost periodicity of compositions of flow homomorphisms
AU - McMahon, D.C.
AU - Woude, van der, J.C.S.P.
AU - Wu, T.S.
PY - 1987
Y1 - 1987
N2 - 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.
AB - 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.
U2 - 10.2140/pjm.1987.128.127
DO - 10.2140/pjm.1987.128.127
M3 - Article
SN - 0030-8730
VL - 128
SP - 127
EP - 148
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
IS - 1
ER -