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 adherent ideal Assume CH Baire function Baire property Bernstein set category base Chapter closed rectangles closed set compact sets contains a perfect contains a region continuum converges COROLLARY countable set decomposition define denote dense set dense-in-itself disjoint sets ensembles equivalent essentially everywhere finite Hamel basis Hausdorff measure Hence implies intersection Lebesgue measure zero Lemma Math meager set multiperiodic n>neN natural number nonempty open set nonempty set nonzero obtain open interval open rectangle open set containing open set G perfect set perfect subsets period set positive Lebesgue measure power 2N Proof quotient algebra rare set rational linear combinations rational number real numbers representable satisfies CCC second category Section set of Lebesgue set of power sets of positive Sierpinski singular set subfamily subregion Suppose Theorem 13 Theorem 20 topology transfinite induction transfinite sequence translation uncountable set