Point Set Theory
Investigations by Baire, Lebesgue, Hausdorff, Marczewski, and othes have culminated invarious schemes for classifying point sets. This important reference/text bringstogether in a single theoretical framework the properties common to these classifications.Providing a clear, thorough overview and analysis of the field, Point Set Theoryutilizes the axiomatically determined notion of a category base for extending generaltopological theorems to a higher level of abstraction ... axiomatically unifies analogiesbetween Baire category and Lebesgue measure . .. enhances understanding of thematerial with numerous examples and discussions of abstract concepts ... and more.Imparting a solid foundation for the modem theory of real functions and associated areas, this authoritative resource is a vital reference for set theorists, logicians, analysts, andresearch mathematicians involved in topology, measure theory, or real analysis. It is anideal text for graduate mathematics students in the above disciplines who havecompleted undergraduate courses in set theory and real analysis
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abundant Baire set abundant everywhere abundant set According to Theorem algebra Applying Assume Baire function Baire property Baire set belongs called category base Chapter closed set compact sets complement conclude condition consequence consisting contains continuous continuum converges COROLLARY countable countable set decomposition define DEFINITION denote determine disjoint element enumeration equality equivalent essentially establish everywhere dense EXAMPLE exists fact finite function f Fund given Hamel basis Hence hold ideal implies induction infinite intersection invariant least Lebesgue measure zero limit linear mapping Math meager set natural number nonzero obtain one-to-one ordinal number perfect set period Proof Proposition real numbers region representable respectively result satisfies CCC second category Section sequence set containing Sierpiński singular set subset Suppose Theorem Theorem 13 Theory topology transfinite sequence translation uncountable uncountable set union