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Gaps and limits are two phenomena occuring in the Boolean algebra P(&ohgr;)/fin. Both were discovered by F. Hausdorff in the mid 1930's. This book aims to show how they can be used in solving several kinds of mathematical problems and to convince the reader that they are of interest in themselves. The forcing technique, which is not commonly known, is used widely in the text. A short explanation of the forcing method is given in Chapter 11. Exercises, both easy and more difficult, are given throughout the book.

Algebra, Boolean. --- Stone-Čech compactification. --- Stone-éCech compactification. --- Boolean algebras. --- Stone-Cech compactification.

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Analytical spaces --- Sobolev spaces --- Sobolev, Espaces de --- 517.987 --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Sobolev spaces. --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems

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517.987 --- 519.713 --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- 519.713 Automata --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Automata --- Number theory

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Mechanics, Analytic. --- Celestial mechanics --- 517.987 --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Mechanics, Analytic --- Mécanique analytique --- Mécanique céleste

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517.987 --- Bifurcation theory --- Differential equations, Nonlinear --- -Differential equations, Partial --- -Partial differential equations --- Nonlinear differential equations --- Nonlinear theories --- Stability --- Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Numerical solutions --- Bifurcation theory. --- Differential equations, Partial --- Numerical solutions. --- -Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- 517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- -517.987 Measures. Representations of Boolean algebras. Metric theory of dynamic systems --- Partial differential equations --- Numerical analysis