Furstenberg Families And Ellis Semigroups

In topological dynamics, Furstenberg families and Ellis semigroups are two essential tools. In this thesis we focus mainly on the relations between them and their applications in topological dynamics. We first introduce some basic properties of Furstenberg families and Ellis semigroups and their relationships, then discuss distal and adherence in the viewpoint of family.This thesis is divided into six chapters, as follows:Chapterl introduces relat-ed backgrounds and basic concepts, Chapter2gives thick family and its relations with ideals, Chapter3proves IP-set and its relation with semigroup and idempo-tent, Chapter4discusses proximity and its relation with idempotent. Chapter5and Chapter6study distality and adherence in the viewpoint of family.