On Almost periodicity and minimality for semiflows

TL;DR

This paper explores the relationship between almost periodicity and minimality in topological semiflows, highlighting differences from group actions and discussing implications when all points are almost periodic.

Contribution

It clarifies the equivalence of almost periodicity and minimality in semiflows and examines the special case where all points are almost periodic.

Findings

Contrasts between semigroup/monoid actions and group actions in topological dynamics.

Conditions under which almost periodicity and minimality are equivalent.

Implications of every point being almost periodic.

Abstract

In topological dynamics, the dynamical behavior sometimes has a sharp contrast when the action is by semigroups or monoids to when the action is by groups. In this article we bring out this contrast while discussing the equivalence of almost periodicity and minimality, and some implications when every point is an almost periodic point.