By J. van Mill
Techniques from basic topology, infinite-dimensional topology, useful research and descriptive set theory
are essentially used for the examine of those areas. the combo of
methods from a number of disciplines makes the subject
particularly fascinating. between different issues, a whole and self-contained facts of the Dobrowolski-Marciszewski-Mogilski Theorem that every one functionality areas of low Borel complexity are topologically homeomorphic, is gifted.
In order to appreciate what's going, an outstanding heritage in
infinite-dimensional topology is required. And for reasonable volume of data of measurement conception in addition to ANR conception is required. the mandatory fabric used to be partly coated in our prior publication `Infinite-dimensional topology, must haves and introduction'. a range of what was once performed there are available the following besides, yet thoroughly revised and at many areas accelerated with contemporary effects. A `scenic' direction has been selected in the direction of the
Dobrowolski-Marciszewski-Mogilski Theorem, linking the
results wanted for its evidence to fascinating contemporary study advancements in measurement thought and infinite-dimensional topology.
The first 5 chapters of this publication are meant as a textual content for
graduate classes in topology. For a path in measurement conception, Chapters 2 and three and a part of bankruptcy 1 will be lined. For a path in infinite-dimensional topology, Chapters 1, four and five. In bankruptcy 6, which bargains with functionality areas, contemporary examine effects are mentioned. it might probably even be used for a graduate direction in topology yet its taste is extra that of a study monograph than of a textbook; it really is therefore
more appropriate as a textual content for a learn seminar. The book
consequently has the nature of either textbook and a learn monograph. In Chapters 1 via five, except stated
otherwise, all areas below dialogue are separable and
metrizable. In bankruptcy 6 effects for extra common sessions of areas are awarded.
In Appendix A for simple reference and a few uncomplicated proof which are vital within the publication were accrued. The ebook isn't meant as a foundation for a direction in topology; its goal is to assemble wisdom approximately common topology.
The workouts within the e-book serve 3 reasons: 1) to check the reader's realizing of the cloth 2) to provide proofs of statements which are utilized in the textual content, yet are usually not confirmed there
3) to supply additional info now not lined by way of the text.
Solutions to chose workouts were incorporated in Appendix B.
These workouts are very important or difficult.
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