Mathematical Methods for Economic Theory 1 [Hardcover]

This two-volume work functions both as a textbook for graduates and as a reference for economic scholars. Assuming only the minimal mathematics background required of every second-year graduate, the two volumes provide a self-contained and careful development of mathematics through locally convex topological vector spaces, and fixed-point, separation, and selection theorems in such spaces. Volume One covers basic set theory, sequences and series, continuous and semi-continuous functions, an introduction to general linear spaces, basic convexity theory, and applications to economics.Set Theory and Properties of Rn.- Set-Theoretic Notation and Concepts.- Properties of The Real Numbers.- Binary Relations.- Euclidean Norm and Metric.- Open and Closed Sets in Rn.- Relatively Open and Closed Sets.- Some Linear Space Properties of Rn.- Sequences and Infinite Series.- Sequences of Real Numbers.- Subsequences and Cauchy Sequences.- Infinite Series.- Efficient Intertemporal Allocation.- Sequences and Series in Rn.- Continuity.- Continuous Vector-Valued Functions.- Continuity and Compactness.- Semi-Continuous Functions.- Limits Inferior and Superior of a Function.- Transformation Functions.- Production and Cost Functions.- Sequences of Functions and Limits.- Linear Spaces.- Introduction.- Linear Combinations and Subspaces.- Linear Transformations and Functionals.- Normed Linear Spaces.- Inner Product Spaces.- Product Spaces and Direct Sums.- Affine Sets.- Convex Sets and Functions.- Convex Sets.- Relative Interiors of Convex Sets.- Extreme Points of a Convex Set.- Minimum Distance and Projection Theorems.- Basic Separation Theorems in Rn.- Convex and Concave Functions.- Continuity of Convex Functions.- Quasi-Concave Functions.- Applications of Convexity.- Introduction.- Basic Production and Cost Theory.- Distance and Support Functions.- Duality lÃL