Groupoid Metrization Theory [electronic resource] : With Applications to Analysis on Quasi-Metric Spaces and Functional Analysis / by Dorina Mitrea, Irina Mitrea, Marius Mitrea, Sylvie Monniaux.

Introduction -- Semigroupoids and Groupoids -- Quantitative Metrization Theory -- Applications to Analysis on Quasi-Metric Spaces -- Non-Locally Convex Functional Analysis -- Functional Analysis on Quasi-Pseudonormed Groups -- References -- Symbol Index -- Subject Index -- Author Index.

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.