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These lecture notes begin with an introduction to topological groups and proceed to a proof of the important Pontryagin-van Kampen duality theorem and a detailed exposition of the structure of locally compact abelian groups. Measure theory and Banach algebra are entirely avoided and only a small amount of group theory and topology is required, dealing with the subject in an elementary fashion. With about a hundred exercises for the student, it is a suitable text for first-year graduate courses.
Locally compact Abelian groups. --- Duality theory (Mathematics) --- Algebra --- Mathematical analysis --- Topology --- Compact Abelian groups --- Locally compact groups --- Topological groups --- Groupes abéliens localement compacts --- Locally compact Abelian groups --- Pontrjagin duality --- 517.986.6 --- Pontryagin duality --- 517.986.6 Harmonic analysis of functions of groups and homogeneous spaces --- Harmonic analysis of functions of groups and homogeneous spaces --- Pontrjagin duality. --- Topological groups. Lie groups --- Duality theory (Mathematics). --- Groupes abéliens localement compacts. --- Groupes topologiques --- Groupes localement compacts
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Algebraic topology --- 515.1 --- Topology --- 515.1 Topology --- Duality theory (Mathematics) --- Piecewise linear topology --- Surgery (Topology) --- Dualité, Principe de (Mathématiques) --- Topologie linéaire par morceaux --- Chirurgie (Topologie) --- Surgery (Topology). --- Duality theory (Mathematics). --- Piecewise linear topology. --- Topologie differentielle
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Bornologies and functional analysis
Functional analysis --- Functional analysis. --- Bornological spaces. --- Duality theory (Mathematics) --- Differential equations, Partial. --- Duality theory (Mathematics). --- Partial differential equations --- Algebra --- Mathematical analysis --- Topology --- Spaces, Bornological --- Linear topological spaces --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Bornological spaces --- Differential equations, Partial --- 517.982 --- 517.982 Linear spaces with topology and order or other structures --- Linear spaces with topology and order or other structures
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Electromagnetic theory --- Relativity (Physics) --- Wave theory of light --- Gravitation --- Nonrelativistic quantum mechanics --- Space and time --- Light, Electromagnetic theory of --- Electric fields --- Magnetic fields --- Light, Wave theory of --- Optics --- Wave-motion, Theory of --- Wave-particle duality
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Functional analysis --- Measure theory. Mathematical integration --- Duality theory (Mathematics) --- Measure theory --- Vector-valued measures --- Measures, Vector-valued --- Radon measures --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Algebra --- Mathematical analysis --- Topology --- Measure theory. --- Vector-valued measures. --- Mesures vectorielles. --- Mesure, Théorie de la. --- Dualité, Principe de (mathématiques)
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