  In [arXiv:1904.12333], we introduced the concept of escaping set in general
setting for a topological space and extended the notion of limit set and
escaping set for the general semigroup generated by continuous self maps. In
this paper we continue with extending the other notions of recurrence for the
generalized semigroup analogs to their counterpart in the classical theory of
dynamics. We discuss the concept of periodic point, nonwandering point and
chain recurrent point in the more general setting of a semigroup and establish
the correlation between them.
