Regionally almost periodic transformation groups

1967 ◽  
Vol 1 (3) ◽  
pp. 257-262 ◽  
Author(s):  
Leonard Bidwell
Keyword(s):  
Transformation Groups ◽  
Almost Periodic ◽  
Periodic Transformation

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.

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).

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