Jobst Heitzig

(Author)

Distance and Topology- Back to the Roots of Topology with a General Concept of DistancePaperback, 11 September 2007

Distance and Topology- Back to the Roots of Topology with a General Concept of Distance
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Print Length
160 pages
Language
English
Publisher
VDM Verlag Dr. Mueller E.K.
Date Published
11 Sep 2007
ISBN-10
3836433125
ISBN-13
9783836433129

Description

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.

Product Details

Author:
Jobst Heitzig
Book Format:
Paperback
Country of Origin:
US
Date Published:
11 September 2007
Dimensions:
24.41 x 16.99 x 0.86 cm
ISBN-10:
3836433125
ISBN-13:
9783836433129
Language:
English
Location:
Saarbrucken
Pages:
160
Weight:
263.08 gm

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