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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Topological Vector Spaces I (Paperback, Softcover reprint of the original 1st ed. 1983)
Loot Price: R3,662
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Topological Vector Spaces I (Paperback, Softcover reprint of the original 1st ed. 1983)
Series: Grundlehren der mathematischen Wissenschaften, 159
Expected to ship within 10 - 15 working days
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It is the author's aim to give a systematic account of the most im
portant ideas, methods and results of the theory of topological
vector spaces. After a rapid development during the last 15 years,
this theory has now achieved a form which makes such an account
seem both possible and desirable. This present first volume begins
with the fundamental ideas of general topology. These are of
crucial importance for the theory that follows, and so it seems
necessary to give a concise account, giving complete proofs. This
also has the advantage that the only preliminary knowledge required
for reading this book is of classical analysis and set theory. In
the second chapter, infinite dimensional linear algebra is
considered in comparative detail. As a result, the concept of dual
pair and linear topologies on vector spaces over arbitrary fields
are intro duced in a natural way. It appears to the author to be of
interest to follow the theory of these linearly topologised spaces
quite far, since this theory can be developed in a way which
closely resembles the theory of locally convex spaces. It should
however be stressed that this part of chapter two is not needed for
the comprehension of the later chapters. Chapter three is concerned
with real and complex topological vector spaces. The classical
results of Banach's theory are given here, as are fundamental
results about convex sets in infinite dimensional spaces."
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