### J. van Mill's The Infinite-Dimensional Topology of Function Spaces PDF

By J. van Mill

ISBN-10: 0444505571

ISBN-13: 9780444505576

During this e-book we examine functionality areas of low Borel complexity. ideas from basic topology, infinite-dimensional topology, practical research and descriptive set idea are basically used for the examine of those areas. the combo of equipment from a number of disciplines makes the topic relatively fascinating. between different issues, an entire and self-contained facts of the Dobrowolski-Marciszewski-Mogilski Theorem that each one functionality areas of low Borel complexity are topologically homeomorphic, is gifted. with a view to comprehend what's going, a pretty good history in infinite-dimensional topology is required. And for reasonable quantity of data of size idea in addition to ANR idea is required. the required fabric used to be in part coated in our prior booklet `Infinite-dimensional topology, necessities and introduction'. a variety of what used to be performed there are available the following besides, yet thoroughly revised and at many areas extended with contemporary effects. A `scenic' path has been selected in the direction of the Dobrowolski-Marciszewski-Mogilski Theorem, linking the consequences wanted for its facts to attention-grabbing contemporary learn advancements in size thought and infinite-dimensional topology. the 1st 5 chapters of this ebook are meant as a textual content for graduate classes in topology. For a direction in measurement thought, Chapters 2 and three and a part of bankruptcy 1 may be coated. For a path in infinite-dimensional topology, Chapters 1, four and five. In bankruptcy 6, which offers with functionality areas, fresh examine effects are mentioned. it may well even be used for a graduate path in topology yet its taste is extra that of a study monograph than of a textbook; it truly is as a result better as a textual content for a study seminar. The booklet therefore has the nature of either textbook and a study monograph. In Chapters 1 via five, except acknowledged another way, all areas less than dialogue are separable and metrizable. In bankruptcy 6 effects for extra common periods of areas are provided. In Appendix A for simple reference and a few uncomplicated evidence which are very important within the publication were amassed. The booklet isn't meant as a foundation for a direction in topology; its goal is to assemble wisdom approximately common topology. The routines within the publication serve 3 reasons: 1) to check the reader's figuring out of the cloth 2) to provide proofs of statements which are utilized in the textual content, yet are usually not confirmed there three) to supply additional info now not lined via the textual content. options to chose workouts were incorporated in Appendix B. those routines are vital or tricky.