Название: Introduction to Topology and Modern Analysis, Reprint Edition Автор: George F. Simmons Издательство: Robert E. Krieger Publishing Company Год: 1983 Формат: PDF Для сайта:Mirknig.su Страниц: 384 Размер: 14,45 МБ Язык: English
For some time now, topology has been firmly established as one of the basic disciplines of pure mathematics. Its ideas and methods have transformed large parts of geometry and analysis almost beyond recognition. It has also greatly stimulated the growth of abstract algebra. As things stand today, much of modern pure mathematics must remain a closed book to the person who does not acquire a working knowledge of at least the elements of topology.
There are many domains in the broad field of topology, of which the following are only a few: the homology and cohomology theory of complexes, and of more general spaces as well; dimension theory; the theory of differentiable and Riemannian manifolds and of Lie groups; the theory of continuous curves; the theory of Banach and Hilbert spaces and their operators, and of Banach algebras; and abstract harmonic analysis on locally compact groups. Each of these subjects starts from roughly the same body of fundamental knowledge and develops its own methods of dealing with its own characteristic problems. The purpose of Part 1 of this book is to make available to the student this “hard core” of fundamental topology; specifically, to make it available in a form which is general enough to meet the needs of modern mathematics, and yet is unburdened by excess baggage best left in the research journals.