Vol. 65, No. 1, 1976

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On the construction of one-parameter semigroups in topological semigroups

John Yuan

Vol. 65 (1976), No. 1, 285–292
Abstract

Let S be a topological Hausdorff semigroup and s S be a strongly root compact element. Then there are an algebraic morphism f : Q+ ∪{0}→ S with f(0) = e, f(1) = s, and a one-parameter semigroup ϕ : H S which satisfy the following properties: If K = ∩{f(]0,𝜖[Q) : 0 < 𝜖 < 1}, then K is a compact connected abelian subgroup of (e), ϕ(0) = e, ϕ(H) is in the centralizer Z = {x eSe : xk = kx for all k K} of K in eSe, and ϕ(t) f(t)K for each t Q+. Furthermore, if 𝒰 is any neighborhood of s in S, then ϕ may be chosen so that ϕ(1) ∈𝒰: and, in fact, if K is arcwise connected, then ϕ may be chosen so that ϕ(1) = s. The above statements also hold for strongly p-th root compact elements almost everywhere.

Mathematical Subject Classification 2000
Primary: 22A15
Secondary: 60B15
Milestones
Received: 13 November 1975
Revised: 9 February 1976
Published: 1 July 1976
Authors
John Yuan