Abstract
Semi-flows or semi-dynamical systems (SDS) are defined only for future time. Natural examples of SDS are provided by functional differential equations for which existence and uniqueness conditions hold. The SDS theory not only generalizes a substantial part of the dynamical systems theory but also gives rise to many new and interesting notions—for example, of a start point. This chapter discusses some properties of start points' sets. For a family of SDS, their product SDS is defined in a natural way. It is possible for none of the factor SDS to have a start point, but the product SDS contains start points. This gives rise to the notion of an improper start point. The chapter explores the conditions for the set of proper/improper start points to be everywhere dense. It also focuses on some of the connectedness properties of the sets of proper/improper start points.
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