This book is based on lectures I have given to undergraduate and
graduate audiences at Oxford and elsewhere over the years. My aim
has been to provide an outline of both the topological theory and
the uniform theory, with an emphasis on the relation between the
two. Although I hope that the prospec tive specialist may find it
useful as an introduction it is the non-specialist I have had more
in mind in selecting the contents. Thus I have tended to avoid the
ingenious examples and counterexamples which often occupy much
ofthe space in books on general topology, and I have tried to keep
the number of definitions down to the essential minimum. There are
no particular pre requisites but I have worked on the assumption
that a potential reader will already have had some experience of
working with sets and functions and will also be familiar with the
basic concepts of algebra and analysis. There are a number of fine
books on general topology, some of which I have listed in the
Select Bibliography at the end of this volume. Of course I have
benefited greatly from this previous work in writing my own
account. Undoubtedly the strongest influence is that of Bourbaki's
Topologie Generale 2], the definitive treatment of the subject
which first appeared over a genera tion ago."
General
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