Theory of Topological Structures

An Approach to Categorical Topology

  • Gerhard Preuss

Part of the Mathematics and Its Applications book series (MAIA, volume 39)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Gerhard Preuss
    Pages 1-2
  3. Gerhard Preuss
    Pages 3-15
  4. Gerhard Preuss
    Pages 16-46
  5. Gerhard Preuss
    Pages 47-89
  6. Gerhard Preuss
    Pages 134-151
  7. Gerhard Preuss
    Pages 152-199
  8. Gerhard Preuss
    Pages 200-241
  9. Gerhard Preuss
    Pages 242-268
  10. Back Matter
    Pages 269-304

About this book


Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.


algebra cohomology ring theory topology

Authors and affiliations

  • Gerhard Preuss
    • 1
  1. 1.Department of MathematicsFree University BerlinGermany

Bibliographic information

  • DOI
  • Copyright Information Springer Science+Business Media B.V. 1988
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-7786-6
  • Online ISBN 978-94-009-2859-6
  • Buy this book on publisher's site