In the disciplines such as image processing, fuzzy mathematics, topological dynamic systems, probability theory, etc., many natural function spaces have been proposed. Over the last two decades, there have been many related research achievements.  This book systematically exhibits some of these achievements with the traditional and new techniques from infinite-dimensional topology as the unifying theme, together with many related open problems for future study. It is potentially useful for these disciplines to have at hand the topological structures of these function spaces. 

Students and researchers in infinite-dimensional topology will find new research problems with practical background in this book. Experts in image processing, fuzzy mathematics, topological dynamic systems, probability theory etc, might get new insights from the material in this book, especially the topological results for each topic.