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ENCYCLOPEDIA OF GENERAL TOPOLOGY
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To order this title, and for more information, click here
By
K.P. Hart, Delft University of Technology, Faculty of Information, Technology and Systems, The Netherlands
Jun-iti Nagata, Uzumasa, Osaka, Japan
J.E. Vaughan, University of North Carolina, Department of Mathematics, Greensboro, NC, USA
Preface & Foreword
General Topology has experienced rapid growth during the past fifty
years, and nowadays its language and concepts pervade much of modern day
mathematics.
This book is intended for a broad community of scholars and students working
in mathematics and other areas who want to become acquainted quickly with
the terminology and ideas of General Topology that may be relevant to their
work.
Thus the book provides a source where the specialist and non-specialist alike
can find short introductions to both the basic theory and the newest
developments in General Topology.
Because the book is designed for the reader who wants to get a general view
of the terminology with minimal time and effort there are very few proofs
given; on occasion a sketch of an argument will be given, more to illustrate
a notion than to justify a claim.
We assume that the reader has a
rudimentary knowledge of Set Theory, Algebra and Analysis.
A reader who wants to study the subject matter of one or more of the articles
systematically (or who wants to see the proof of a particular result)
will find sufficient references at the end of each
article as well as in the books in our list of standard references.
Guide to the reader.
Titles of articles are given in the Table of Contents under the following ten
headings that roughly follow Section 54 of the 2000 Mathematics Subject
Classification as used by Mathematical Reviews and Zentralblatt MATH.
• A - Generalities
• B - Basic constructions
• C - Maps and general types of spaces defined by maps
• D - Fairly general properties
• E - Spaces with richer structures
• F - Special properties
• G - Special spaces
• H - Connection with other structures
• J - Influences of other fields
• K - Connections with other fields
Topological terms used in the encyclopedia are listed in the Index.
Terms defined within an article are indicated like so: compactness.
Terms used in an article but defined elsewhere will be typeset thus:compactness (the first occurrence only); their definitions can be
located by consulting the index.
There is a list of standard references, given below, that are cited uniformly
by a letter system. Thus [E, 3.1] would refer to the first section on
compactness in Engelking's General Topology and [HvM, Chapter 18]
to the chapter on compact spaces in Recent Progress in General
Topology (edited by Husek and van Mill).
[E]Ryszard Engelking, General topology, second ed., Sigma Series in Pure
Mathematics, no.6, Heldermann Verlag, Berlin, 1989.
[HvM] Miroslav Husek and Jan van Mill (eds.), Recent progress in general
topology, North-Holland Publishing Co., Amsterdam, 1992.
[Ke] John L. Kelley, General topology, D. Van Nostrand Company, Inc.,
Toronto-New York-London, 1955. Reprinted as: Graduate Texts in Mathematics,
No. 27, Springer-Verlag, New York, 1975.
[Ku] Kenneth Kunen, Set theory. An introduction to independence proofs,
Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland
Publishing Co., Amsterdam, 1980.
[KV] Kenneth Kunen and Jerry E. Vaughan (eds.), Handbook of set-theoretic
topology, North-Holland Publishing Co., Amsterdam, 1984.
[KI] K. Kuratowski, Topology. Vol. I, Academic Press, New York, 1966.
[KII] Topology. Vol. II, Academic Press, New York, 1968.
[Kur] Introduction to set theory and topology,
PWN - Polish Scientific Publishers and Pergamon Press, Warsaw and Oxford-New
York-Toronto, Ont., 1977.
[vMR] Jan van Mill and George M. Reed (eds.), Open problems in topology,
North-Holland Publishing Co., Amsterdam, 1990.
[MN] Kiiti Morita and Jun-iti Nagata (eds.), Topics in general topology,
North-Holland Mathematical Library, vol. 41, North-Holland Publishing Co.,
Amsterdam, 1989.
Jun-iti Nagata, Modern general topology, second ed., North-Holland
Mathematical Library, vol.~33, North-Holland Publishing Co., Amsterdam, 1985.
Acknowledgments
We wish to thank Professor W. Moors for his help with the English expression of
some of the articles,
Professor K. Yamada for his help in various ways,
the Symposium of General Topology of Japan for partial financial support,
Professor A. V. Arhangel'skii for
his help organizing the articles related to Cp
(X)-theory, and
Drs. A. Sevenster for his
encouragement throughout the project.
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