Mathematical methods for economic theory 2
This textbook is the second of a two-volume work (for Vol. 1 see the review Zbl 0936.91001 above) intended to graduate students in economics as well as a reference work for economic scholars with a strong interest in microeconomic theory. The required mathematical background corresponds to that of a second-year graduate student in economics. In each section, there are one or more entries labeled `Examples/Exercises', as well as exercises at the end of each section. The exercises at the end of a section are for the purpose of providing a self-test. The exercises are arranged in order of difficulty. The author recommends that the student should work through at least the first two or three of the exercises at the end of a given section before tackling the next section. Volume 2 covers six sections, numbered from 7 to 12: Section 7: Introduction to topology with basic concepts, closed sets and closures, topological bases, continuous functions, complete metric spaces, nets and convergence. Section 8: Additional topics in topology, relative anti product topologies, Hausdorff and normal spaces, connected spaces paracompactness anti partitions of unity. Section 9: Correspondences; hemi-continuous and closed correspondences, domain and range of correspondences, correspondences into metric spaces, open correspondences and open sections. Section 10: Banach spaces; bounded linear mappings, same fundamental theorems, dual spaces. Section 11: Topological vector spaces; continuous functions and convex sets, separation theorems, equilibrium models in Hilbert space, locally convex spaces, correspondences. Section 12: Selection and fixed point theorems; maximum theorems, Sperner's lemma and the \(K\)-\(K\)-\(M\) theorem; equilibrium in an `abstract economy'.
scientific article; zbMATH DE number 1391253