Pseudocompact Topological Spaces

Description

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. Front Matter ....Pages i-xiii Basic and Classic Results on Pseudocompact Spaces (J. Angoa-Amador, A. Contreras-Carreto, M. Ibarra-Contreras, Á. Tamariz-Mascarúa)....Pages 1-38 Pseudocompact Topological Groups (M. Tkachenko)....Pages 39-76 Pseudocompactness and Ultrafilters (S. García-Ferreira, Y. F. Ortiz-Castillo)....Pages 77-105 Bounded Subsets of Tychonoff Spaces: A Survey of Results and Problems (M. Sanchis)....Pages 107-150 Weakly Pseudocompact Spaces (A. Dorantes-Aldama, O. Okunev, Á. Tamariz-Mascarúa)....Pages 151-189 Maximal Pseudocompact Spaces (M. Madriz-Mendoza, V. V. Tkachuk, R. G. Wilson)....Pages 191-216 Pseudocompactness in the Realm of Topological Transformation Groups (N. Antonyan, S. Antonyan, M. Sanchis)....Pages 217-252 Topology of Mrówka-Isbell Spaces (F. Hernández-Hernández, M. Hrušák)....Pages 253-289 Back Matter ....Pages 291-299