Introduction to Knot Theory pp 1-2 | Cite as

# Prerequisites

- 1.8k Downloads

## 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 *R*^{ n }; 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.