Almost periodicity and discrete almost periodicity in semiflows

A theory of semiflows with a discrete acting topological semigroup was developed in the 2000 paper by D. Ellis, R. Ellis and M. Nerurkar ([2]). A theory for the case of an arbitrary acting topological semigroup has still to be developed. This paper can be considered as the beginning of an attempt in that direction. We discuss almost periodicity and G-almost periodicity of points in a semiflow and end the paper with an adaptation to the semiflows of the 1998 theorem of Pestov for flows about independence of almost periodicity of a point upon the topology of the acting group ([6]). AMS subject classifications: 37B05, 54H20