Almost Periodic Homeomorphisms and p-Adic Transformation Groups on Compact 3-Manifolds

1994 ◽  
Vol 121 (1) ◽  
pp. 267 ◽  
Author(s):  
Joo S. Lee
Keyword(s):  
Transformation Groups ◽  
Almost Periodic

Recurrent Transformation Groups

1969 ◽  
Vol 21 ◽  
pp. 564-575
Author(s):  
R. A. Christiansen
Keyword(s):  
Topological Space ◽  
Transformation Groups ◽  
Sufficient Condition ◽  
Almost Periodic ◽  
Compact Topological Space ◽  
Trivial Subgroup

Let (X, T, π) denote a flow, whereXis a compact topological space metrizable byd, andTis a closed non-trivial subgroup of the reals under addition.Tisrecurrentif and only if for eachands> 0, there existst>ssuch thatx∈Ximplies. IfTis almost-periodic, thenTis both recurrent and distal. In§§4 and 5, it is shown that, under more stringent hypotheses, the recurrence ofTis neither a necessary nor a sufficient condition forTto be distal. LetSbe a closed non-trivial subgroup ofT. It is shown in§3 thatTis recurrent if and only ifSis recurrent. From this result, we obtain a solution to a problem posed by Nemyckiĭ (16, p. 492, Problem 6).

scholarly journals On locally weakly almost periodic transformation groups

1982 ◽  
Vol 25 (2) ◽  
pp. 215-219
Author(s):  
Saber Elaydi
Keyword(s):  
Phase Space ◽  
Transformation Group ◽  
Transformation Groups ◽  
Almost Periodic ◽  
Locally Compact ◽  
Weakly Almost Periodic ◽  
Phase Group ◽  
Periodic Transformation

It is shown that a transformation group with a locally compact Hausdorff phase space and an abelian phase group is locally weakly almost periodic if and only if it is P-locally weakly almost periodic for some replete semigroup P in the phase group.

Equicontinuity and -recursive transformation groups

1965 ◽  
Vol 61 (2) ◽  
pp. 333-336 ◽  
Author(s):  
Janet Allsbrook ◽  
R. W. Bagley
Keyword(s):  
Phase Space ◽  
Transformation Group ◽  
Transformation Groups ◽  
Almost Periodic ◽  
Convergence Space ◽  
Topological Transformation ◽  
Uniform Convergence Space ◽  
Left And Right ◽  
Uniformly Continuous ◽  
Special Case

In this paper we obtain results on equicontinuity and apply them to certain recursive properties of topological transformation groups (X, T, π) with uniform phase space X. For example, in the special case that each transition πt is uniformly continuous we consider the transformation group (X,Ψ,ρ), where Ψ is the closure of {πt|t∈T} in the space of all unimorphisms of X onto X with the topology of uniform convergence (space index topology) and p(x, φ) = φ(x) for (x, φ)∈ X × Ψ. (See (1), page 94, 11·18.) If π is a mapping on X × T we usually write ‘xt’ for ‘π(x, t)’ and ‘AT’ for ‘π(A × T)’ where A ⊂ X. In this case we obtain the following results:I. If (X, T, π) is almost periodic [regularly almost periodic] and πxis equicontinuous, then (X,Φ,ρ) is almost periodic [regularly almost periodic]II. Let A be a compact subset of X such that. If the left and right uniformities of T are equal and (X, T, π) is almost periodic [regularly almost periodic], then (X, T, π) is almost periodic [regularly almost periodic].

scholarly journals Relations between Non-Compact Transformation Groups and Compact Transformation Groups

1971 ◽  
Vol 44 ◽  
pp. 97-117
Author(s):  
Hsin Chu
Keyword(s):  
Fundamental Group ◽  
Transformation Group ◽  
Fibre Bundle ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Transformation Groups ◽  
Almost Periodic ◽  
Minimal Set ◽  
Weakly Almost Periodic ◽  
Necessary And Sufficient

In this paper certain relations between non-compact transformation groups and compact transformation groups are studied. The notion of re-ducibility and separability of transformation groups is introduced, several necessary and sufficient conditions are established: (1) A separable transformation group to be locally weakly almost periodic, (2) A reducible and separable transformation group to be a minimal set and (3) A reducible and separable transformation group to be a fibre bundle. As applications we show, among other things, that (1) for certain reducible transformation groups its fundamental group is not trivial which is a generalization of a result in [4].

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