Prerequisites

Abstract

For an intelligent reading of this book a knowledge of the elements of modern algebra and point-set topology is sufficient. Specifically, we shall assume that the reader is familiar with the concept of a function (or mapping) and the attendant notions of domain, range, image, inverse image, one-one, onto, composition, restriction, and inclusion mapping; with the concepts of equivalence relation and equivalence class; with the definition and elementary properties of open set, closed set, neighborhood, closure, interior, induced topology, Cartesian product, continuous mapping, homeomorphism, compactness, connectedness, open cover(ing), and the Euclidean n-dimensional space Rⁿ; and with the definition and basic properties of homomorphism, automorphism, kernel, image, groups, normal subgroups, quotient groups, rings, (two-sided) ideals, permutation groups, determinants, and matrices. These matters are dealt with in many standard textbooks. We may, for example, refer the reader to A. H. Wallace, An Introduction to Algebraic Topology (Pergamon Press, 1957), Chapters I, II, and III, and to G. Birkhoff and S. MacLane, A Survey of Modern Algebra, Revised Edition (The Mac-millan Co., New York, 1953), Chapters III, §§1–3, 7, 8; VI, §§4–8, 11–14; VII, §5; X, §§1, 2; XIII, §§1–4. Some of these concepts are also defined in the index.