IOSPress

This book deals with two unrelated topics. Chapter 1 gives a consistency proof on the minimal cardinality of certain sets of continuous self maps of the Cantor set, the remaining chapters investigate how certain properties of continua (connected compact Hausdorff spaces) relate to their lattices of closed subsets.
In the second part, which covers the chapters 2,3,4 and 5, the author uses Wallman’s representation theorem on lattices to investigate, by model theoretic means, how certain properties of compact Hausdorff spaces relate to the lattice of their closed sets. He is particularly interested in the class of continua (connected, compact Hausdorff spaces).