Point Set Theory

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CRC Press, Oct 23, 1989 - Mathematics - 296 pages
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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Contents

Preface V
1
PointMeager and Baire Bases
70
Separable Bases
102
Cluster Points and Topologies
112
Perfect Bases
144
Translation Bases
192
Bibliography
251
Index
276
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Page 261 - On the method of transfinite indices in the theory of operations on sets. Proc. Steklov Inst. Math.

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