Basic Analysis – Gently Done Topological Vector Spaces

Preface
These notes form an enhanced version of the lecture notes for the M. Sc. course,
Basic Analysis, presented in the Department of Mathematics at King’s College,
London. It is a pleasure to thank Dr. Frank Jellett for many enjoyable discussions.
The following books might serve as a good starting point for those wishing to find
out more. (For example, Wilansky’s book includes a set of 33 tables of theorems
and counterexamples, as well as 1500 problems.)
R. V. Kadison and J. R. Ringrose, Fundamentals of the Theory of Operator
Algebras, Vol. 1, Academic Press, 1983, and Vol. 3, Birkhäuser Boston, 1990
J. L. Kelley, General Topology, D. Van Nostrand, Princeton, New Jersey, 1955;
reprinted, Springer-Verlag, New York, 1975
I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, 2nd
edition, 1988
J. R. Munkres, Topology—A First Course, Prentice Hall, 1975
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 1
Functional Analysis, Academic Press, revised and enlarged edition, 1980
A. P. Robertson and W. Robertson, Topological Vector Spaces, Cambridge University
Press, 1964
W. Rudin, Functional Analysis, McGraw-Hill, 2nd edition, 1973
G. F. Simmons, Introduction to Topology and Modern Analysis, McGraw-Hill,
1963
A. E.Taylorand D. C. Lay,Introduction to Functional Analysis,Wiley,New York,
1980
A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, 1978
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Ivan F. Wilde