Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces

2013 ◽  
Author(s):  
Toka Diagana
Keyword(s):  
Almost Periodic ◽  
Almost Automorphic ◽  
Abstract Spaces

Continuity properties of compact right topological groups

1979 ◽  
Vol 86 (3) ◽  
pp. 427-435 ◽  
Author(s):  
Paul Milnes
Keyword(s):  
Almost Periodic ◽  
Periodic Functions ◽  
Topological Groups ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Almost Automorphic Functions ◽  
Continuity Properties ◽  
Enveloping Semigroups ◽  
The One ◽  
Automorphic Functions

AbstractCompact right topological groups appear naturally in topological dynamics. Some continuity properties of the one arising as an enveloping semigroup from the distal function are considered here (and, by way of comparison, the enveloping semigroups arising from two almost automorphic functions are discussed). The continuity properties are established either explicitly or by citing a theorem which is proved here and gives some characterizations of almost periodic functions. One characterization is proved using the result (essentially due to W. A. Veech) that a distal, almost automorphic function is almost periodic. A proof of this last result is also given.

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