During this variation, a collection of Supplementary Notes and feedback has been extra on the finish, grouped in line with bankruptcy. a few of these name awareness to next advancements, others upload additional rationalization or extra feedback. lots of the comments are followed by means of a in short indicated evidence, that's occasionally diverse from the only given within the reference brought up. The record of references has been accelerated to incorporate many fresh contributions, however it remains to be no longer meant to be exhaustive. John C. Oxtoby Bryn Mawr, April 1980 Preface to the 1st variation This ebook has major topics: the Baire classification theorem as a mode for proving life, and the "duality" among degree and class. the class process is illustrated by way of various normal purposes, and the analogy among degree and classification is explored in all of its ramifications. To this finish, the weather of metric topology are reviewed and the primary homes of Lebesgue degree are derived. It seems that Lebesgue integration isn't really crucial for current purposes-the Riemann necessary is enough. ideas of basic degree thought and topology are brought, yet not only for the sake of generality. remember the fact that, the time period "category" refers regularly to Baire classification; it has not anything to do with the time period because it is utilized in homological algebra.
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