Theorems and Problems in Functional Analysis: The Answer Book Volume I

Volumes I through V of Theorems and Problems in Functional Analysis: The Answer Book present different techniques for solving the 828 Exercises found in the A.A. Kirillov and Gvichiani book, entitled Theorems and Problems in Functional Analysis. The original book by Kirillov and Gvichiani was in the Problem Book in Mathematics Series, published by Springer. This volume mainly focuses on set theory, order relationships and completeness of spaces with interesting problems about Mobius functions, the p-adic fields and related results from elementary number theory. The last 23 exercises deal with category theory topics, such as constructions of a torsion product, of a Lie algebra with n generators, of tensor product, and so on. This volume also contains a very interesting problem about the homeomorphism between p-adic fields and the Cantor set. Supplementing the book, Theorems and Problems in Functional Analysis, these volumes may be used by graduate students taking a course in functional analysis. In order to understand this text, the reader must be familiar with mathematical analysis and real analysis.