This book, intended for postgraduate students and researchers, presents many results of historical importance on pseudocompact spaces. In 1948, E. Hewitt introduced the concept of pseudocompactness which generalizes a property of compact subsets of the real line. A topological space is pseudocompact if the range of any real-valued, continuous function defined on the space is a bounded subset of the real line. Pseudocompact spaces constitute a natural and fundamental class of objects in General Topology and research into their properties has important repercussions in diverse branches of Mathematics, such as Functional Analysis, Dynamical Systems, Set Theory and Topological-Algebraic structures.

The collection of authors of this volume include pioneers in their fields who have written a comprehensive explanation on this subject. In addition, the text examines new lines of research that have been at the forefront of mathematics. There is, as yet, no text that systematically compiles and develops the extensive theory of pseudocompact spaces, making this book an essential asset for anyone in the field of topology.

Presents many useful results and new notions that cannot be found in existing books and are difficult (or impossible) to find in journal articles Gives special attention to new lines of research Appropriate level for postgraduate students or researchers in general (or set-theoretic) topology Written in a style that is easy to read for both students and experienced researchers in this area Focuses on topological groups and their generalizations, a subject in which there has been a lot of activity the last decades

Autorentext
Michael Hruák is a Professor at the Instituto de Matemáticas at the Universidad Nacional Autónoma de México. His main area of research is set theory and its applications in topolgy, topological groups, and real anaysis.

Inhalt

1. Basic and Classic Results on Pseudocompact Spaces.- 2. Pseudocompact Topological Groups.- 3. Pseudocompactness and Ultrafilters.- 4. Bounded Subsets of Tychonoff Spaces: A Survey of Results and Problems.- 5. Weakly Pseudocompact Spaces.- 6. Maximal Pseudocompact Spaces.- 7. Pseudocompactness in the Realm of Topological Transformation Groups.- 8. Topology of Mrówka-Isbell Spaces.