Combinatorial Topology Volume 1 PDF
Preview Combinatorial Topology Volume 1
P.S. Aleksandrov C O M B I N AT O R I A L T O P O L O G Y Volume 1 COMBINATORIAL TOPOLOGY VOLUME 1 OTHER GRAY LOCK PUBLICATIONS ALEKSANDROV: Combinatorial Topology Vol. 1: Introduction. Complexes. Coverings. Dimension Vol. 2: The Betti Groups Vol. 3: Homological Manifolds. The Duality Theorems. Cohomology Groups of Compacta. Continuous Mappings of Polyhedra KHINCHIN: Three Pearls of Number Theory Mathematical Foundations of Quantum Statistics KOLMOGOROV and FOMIN: Elements of the Theory of Functions and Functional Analysis Vol. 1: Metric and Normed Spaces Vol. 2: Measure. The Lebesgue Integral. Hilbert Space NOVOZHILOV: Foundations of the Nonlinear Theory of Elasticity PETROVSKII: Lectures on the Theory of Integral Equations PONTRYAGIN: Foundations of Combinatorial Topology TIETZE: Famous Problems of Mathematics COMBINATORIAL TOPOLOGY VOLUME 1 BY P. S. ALEKSANDROV G R A Y L O C K P R E S S BALTIMORE, MD. 1956 TRANSLATED FROM THE FIRST (1947) RUSSIAN EDITION BY HORACE KOMM Copyright, 1956, by GRAYLOCK PRESS 428 E. Preston Street Baltimore, Md. 21202 Third Printing, October 1969 All rights reserved. This book, or parts thereof, may not be reproduced in any form, or translated, without permission in writing from the publishers. Library of Congress Catalog Card Number 56-13930 Second Printing January 1965 Manufactured in the United States of America TRANSLATOR’S NOTE This volume is a translation of the first third of P. S. Aleksandrov’s Kombinatornaya Topologiya. An appendix on the analytic geometry of Euclidean n-space is also included. The volume, complete in itself, deals with certain classical problems such as the Jordan curve theorem and the classification of closed surfaces without using the formal techniques of homology theory. The elementary but rigorous treatment of these prob lems, the introductory chapters on complexes and coverings and their applications to dimension theory, and the large number of examples and pictures should provide an excellent intuitive background for further study in combinatorial topology. In Chapter I the references have been expanded to include a number of standard works in English. References to these and to the books and papers cited in Chapter I of the original are listed at the end of the chapter and correspond to the numbers enclosed in brackets in the body of the text. References in the remaining chapters are enclosed in brackets, capital letters referring to books and lower case letters to papers. These refer to the bibliography at the end of the book. The bibliography includes all papers mentioned in the original edition and a few which have been added by the translator. English translations are cited wherever possible. Cross- references to items in the text are made by citing chapter and section. Where the chapter number is omitted, the reference is to a section of the chapter being read. The system of transliteration used is that of the Mathe matical Reviews. This may be confusing only in the cases of Aleksandrov and Tihonov, whose names are usually written in English as Alexandroff and Ty chon off. V 16138
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