Abstract
The reader who has found his (or her) way through the first thousand problems of this book is fully prepared to enjoy working professionally in C p -theory. Such a work implies choosing a topic, reading the papers with the most recent progress thereon and attacking the unsolved problems. Now, the first two steps are possible without doing heavy library work, because Chapter 1 provides information on the latest advances in all areas of C p -theory, where compactness is concerned. Here, many ideas, results and constructions came from functional analysis giving a special flavor to this part of C p -theory, but at the same time making it more difficult to master. I must warn the reader that most topics, outlined in the forthcoming bulk of 500 problems, constitute the material of important research papers—in many cases very difficult ones. The proofs and solutions, given in Chapter 2, are complete, but sometimes they require a very high level of understanding of the matter. The reader should not be discouraged if some proofs seem to be unfathomable. We still introduce new themes in general topology and formulate, after a due preparation, some non-trivial results which might be later used in C p -theory.
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Tkachuk, V.V. (2015). Behavior of Compactness in Function Spaces. In: A Cp-Theory Problem Book. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-16092-4_1
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DOI: https://doi.org/10.1007/978-3-319-16092-4_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-16091-7
Online ISBN: 978-3-319-16092-4
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