Topological and Metric Spaces, Banach Spaces...

...and Bounded Operators - Functional Analysis Examples c-2
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96 pages
In this book you find the basic mathematics that is needed by engineers and university students .
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Om forfatteren

Leif Mejlbro was educated as a mathematician at the University of Copenhagen, where he wrote his thesis on Linear Partial Differential Operators and Distributions. Shortly after he obtained a position at the Technical University of Denmark, where he remained until h...


In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.

Topics as Topological, metric, Hilbert and Banach spaces and Spectral Theory are illustrated.

This book requires knowledge of Calculus 1 and Calculus 2.

This is the second volume containing examples from Functional analysis. The topics here are limited to Topological and metric spaces, Banach spaces and Bounded operators.

Unfortunately errors cannot be avoided in a first edition of a work of this type. However, the author has tried to put them on a minimum, hoping that the reader will meet with sympathy the errors which do occur in the text.

Leif Mejlbro
24th November 2009

  1. Introduction
  2. Topological and metric spaces
    1. Weierstra ’s approximation theorem
    2. Topological and metric spaces
    3. Contractions
    4. Simple integral equations
  3. Banach spaces
    1. Simple vector spaces
    2. Normed spaces
    3. Banach spaces
    4. The Lebesgue integral
  4. Bounded operators
  5. Index