An Introduction to Classical Complex Analysis: Vol. 1 (Mathematische Reihe, Band 64) - Softcover

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to Classical Complex Analysis Vol. 1 by Robert B. Burckel Kansas State University 1979 BIRKHAUSER VERLAG BASEL UND STUTTGART CIP-Kurztitelaufnahme der Deutschen Bibliothek Burckel, Robert B.: An introduction to classical complex analysis I by Robert B. Burckel. - Basel. Stuttgart: Birkhiiuser. Vol. I. - 1979. (Lehrbilcher und Monographien aus dem Gebiete der exakten Wissenschaften: Math. Reihe; Bd. 64) All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the Copyright owner. © Birkhiiuser Verlag Basel, 1979 North and South America Edition published by ACADEMIC PRESS. INC. III Fifth Avenue, New York, New York 10003 (Pure and Applied Mathematics, A Series of Monographs and Textbooks, Volume 82) ISBN-13: 978-3-0348-9376-3 e-ISBN-13: 978-3-0348-9374-9 DOl: 10.1007/978-3-0348-9374-9 Library of Congress Catalog Card Number 78-67403 5 Contents Volume I PREFACE 9 Chapter 0 PREREQUISITES AND PRELIMINARIES 13
1 Set Theory 13
2 Algebra 14
3 The Battlefield 14
4 Metric Spaces 15
5 Limsup and All That 18
6 Continuous Functions 20
7 Calculus 21 Chapter I CURVES, CONNECTEDNESS AND CONVEXITY 22
1 Elementary Results on Connectedness 22
2 Connectedness of Intervals, Curves and Convex Sets 23
3 The Basic Connectedness Lemma 28
4 Components and Compact Exhaustions 29
5 Connectivity of a Set 33
6 Extension Theorems 37 Notes to Chapter I 39

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