Counterexamples in Topological Vector Spaces
- PDF / 8,083,017 Bytes
- 200 Pages / 461 x 684 pts Page_size
- 33 Downloads / 297 Views
936 S. M. Khaleelulla
Counterexamples in Topological Vector Spaces
Springer-Verlag Berlin Heidelberg New York 1982
Author S.M. Khaleelulla Department of Mathematics Faculty of Science, King Abdulaziz University P.O. Box 9028, Jeddah, Saudi Arabia
AMS Subject Classifications (1980): 46A05, 46A06, 46A07, 46A09, 46A14, 46A25, 46A35, 46A40, 46B05, 46B15, 46B30, 46C05, 46H 05, 46J 20 ISBN 3-540-11565-X Springer-Verlag Berlin Heidelberg New York ISBN 0-387-11565-X Springer-Verlag New York Heidelberg Berlin
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to "Verwertungsgesellschaft Wort", Munich.
© by Springer-Verlag Berlin Heidelberg 1982 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140-543210
TO
PROFESSOR GALAL M. EL-SAYYAD
PREFACE During the last three decades much progress has been made in the field of topological vector spaces. Many generalizations have been introduced; this
was, to a certain
extent, due to the curiosity of studying topological vector spaces for which a known theorem of Functional analysis can be proved. To justify that a class C1 of topological vector spaces is a proper generalization of another class C2 of topological vector spaces, it is necessary to construct an example of a topological vector space belonging to C1but not to C2
;
such an example is called a counterexample. In
this book the author has attempted to present such counterexamples in topological vector spaces, ordered topological vector spaces, topological bases and topological algebras. The author makes no claim to completeness, obviously because of the vastness of the subject. He makes no attempt to give due recognition
to the authorship of most of the
counterexamples presented in this book. It is assumed that the reader is familiar with general topology. The reader may refer to
B[18] for information
about general topo10gy. To facilitate the reading of this book, some fundamental concepts in vector spaces and ordered vector spaces have been collected in the Chapter called 'Prerequisites'. Thereafter each Chapter begins with an introduction which presents the relevent definitions and statements of theorems and propositions with references where their proofs can be
VI
found.
For some counterexamples which require long and
complicated proofs, only reference has been made to the literature where they are available.
The books and papers are listed separately in the bibliography at the end of the book.
Any reference to a
book is indicated by writing B [ ] and to a paper by P [
J
The author would like to express his deep gratitude to Professor T. Husain, McMaster University, Hamilton, Canada, and Dr. T. Tweddle, University of Stirling,
Data Loading...
