Distance and Topology- Back to the Roots of Topology with a General Concept of Distance - Softcover

Heitzig, Jobst

Softcover

ISBN 10: 3836433125 ISBN 13: 9783836433129

Publisher: VDM Verlag Dr. Mueller E.K., 2007

Synopsis

The aim of this book is threefold: to reinstate distance functions as a principal tool of general topology, to promote the use of distance functions on various mathematical objects and a thinking in terms of distances also in nontopological contexts, and to make more specific contributions to distance theory. We start by learning the basic properties of distance, endowing all kinds of mathematical objects with a distance function, and studying interesting kinds of mappings between such objects. This leads to new characterizations of many well-known types of mappings. Then a suitable notion of distance spaces is developed, general enough to induce most topological structures, and we study topological properties of mappings like the concept of strong uniform continuity. Important results include a new characterization of the similarity maps between Euclidean spaces, and generalizations of completion methods and fixed point theorems, most notably of the famous one by Brouwer. We close with a short study of distance visualization techniques.

About this title

About the Author

The author was born 1972 in Hannover, Germany, where he studied physics and mathematics. He received a PhD in mathematics for his work on distance functions and has also worked on privacy in statistical databases. He lives in Frankfurt am Main.

Edition details

• Publisher: VDM Verlag Dr. Mueller E.K.
• Publication date: 2007
• Language: English
• ISBN 10: 3836433125
• ISBN 13: 9783836433129
• Binding: Paperback
• Number of pages: 160