Topics on Continua
This book is an important complement to the existing literature on continuum theory. It covers four topics: inverse limits, the Jones set function T, homogenous continua, and n-fold hyperspaces. The book starts with some topology background material (assuming a one year course on general topology). It covers continuous decompositions, the fundamental group and hyperspaces. Chapter 2 is devoted to inverse limits on continua proving commutativity with finite products, cones and hyperspaces. In chapter 3, the Jones set function T is introduced with relations to connectedness “im Kleinen”, i.e. local connectedness. Some applications are presented as well. Chapters 4 and 5 cover homogenous continua. Decomposition theorems are proved using the Jones set function T and the Effros theorem. Some nontrivial examples of homogeneous continua are presented. Chapter 6 is devoted to general properties of n-fold hyperspaces. In chapter 7, the book provides a list of open questions on each topic studied. The book is very well written and will be a useful tool for the continuum theory community and an excellent source of research topics.