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The topics in this research monograph are at the interface of several areas of mathematics such as harmonic analysis, functional analysis, analysis on spaces of homogeneous type, topology, and quasi-metric geometry. The presentation is self-contained with complete, detailed proofs, and a large number of examples and counterexamples are provided. Unique features of Metrization Theory for Groupoids: With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis include: * treatment of metrization from a wide, interdisciplinary perspective, with accompanying applications ranging across diverse fields; * coverage of topics applicable to a variety of scientific areas within pure mathematics; * useful techniques and extensive reference material; * includes sharp results in the field of metrization. Professional mathematicians with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. At the same time, the monograph is accessible and will be of use to advanced graduate students and to scientifically trained readers with an interest in the interplay among topology and metric properties and/or functional analysis and metric properties.

Functional analysis. --- Nonsymmetric matrices. --- Probabilities. --- Quasi-metric spaces. --- Groupoids --- Harmonic analysis --- Functional analysis --- Mathematics --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Physical Sciences & Mathematics --- Algebra --- Operations Research --- Groupoids. --- Harmonic analysis. --- Functional calculus --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Mathematics. --- Algebraic geometry. --- Mathematical analysis. --- Analysis (Mathematics). --- Measure theory. --- Topology. --- Abstract Harmonic Analysis. --- Functional Analysis. --- Analysis. --- Measure and Integration. --- Algebraic Geometry. --- Calculus of variations --- Functional equations --- Integral equations --- Banach algebras --- Calculus --- Mathematical analysis --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Group theory --- Global analysis (Mathematics). --- Geometry, algebraic. --- Algebraic geometry --- Geometry --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- 517.1 Mathematical analysis