Distance and Topology
Back to the Roots of Topology with a General Concept of Distance
(Sprache: Englisch)
The aim of this book is threefold: to reinstate distance functions as a principaltool of general topology, to promote the use of distance functions on variousmathematical objects and a thinking in terms of distances also in nontopologicalcontexts, and to...
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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.
Klappentext zu „Distance and Topology “
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 non-topological 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.
Autoren-Porträt von Jobst Heitzig
Jobst Heitzig was born 1972 in Hannover,Germany, where he studied physics andmathematics. He received a PhD in mathematicsfor his work on distance functions and has alsoworked on privacy in statistical databases. He livesin Frankfurt am Main.
Bibliographische Angaben
- Autor: Jobst Heitzig
- 2007, 160 Seiten, Maße: 17 x 24 cm, Kartoniert (TB), Englisch
- Verlag: VDM Verlag Dr. Müller
- ISBN-10: 3836433125
- ISBN-13: 9783836433129
Sprache:
Englisch
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