Chapter 34 EQUILIBRIUM THEORY IN INFINITE DIMENSIONAL SPACES* ANDREU MAS-COLELL ~ and WILLIAM R. ZAME b aDepartment of Economics, Harvard University bDepartment of Economics, Johns Hopkins University Contents 1. Introduction 1836 2. The essential mathematical structures 1838 3. Basic assumptions 1842 4. Preferences and continuity 1843 5. Prices 1847 6. The main difficulties 1849 6.1. Compactness 1849 6.2. Supportability 1852 6.3. Joint continuity 1853 7. The basic fixed point argument 1854 8. Interior consumption and L~ 1859 9. Properness and general commodity spaces 1864 9.1. One consumer 1864 9.2. Several consumers 1867 10. The order ideal L(w) 1871 11. Separable utilities and the finance model 1874 12. The lattice structure of the price space 1876 13. Other approaches 1879 14. Production 1882 15. Final comments 1888 References 1890 *Support from the National Science Foundation and the Deutsche Forschungsgemeinschaft, Gottfried-Wilhelm-Leibniz-F6rderpreis during BoWo'89 is gratefully acknowledged. Thanks are also due to R.A. Dana, P.K. Monteiro and N. Yannelis for careful reading of the manuscript. Handbook of Mathematical Economics, Volume IV, Edited by W. Hildenbrand and H. Sonnenschein © Elsevier Science Publishers B.V., 1991