Distance and Topology: Back to the Roots of Topology with a General Concept of Distance - Couverture souple

Heitzig, Jobst

 
9783639450446: Distance and Topology: Back to the Roots of Topology with a General Concept of Distance
Couverture souple
ISBN 10 : 3639450442 ISBN 13 : 9783639450446
Editeur : AV Akademikerverlag, 2012

Synopsis

Revision with unchanged content. 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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Revision with unchanged content. 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.

Biographie de l'auteur

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
AV Akademikerverlag
Date d'édition
2012
Langue
anglais
ISBN 10 
3639450442
ISBN 13 
9783639450446
Reliure
Broché
Nombre de pages
164
Coordonnées du fabricant
non disponible
Personne responsable
info@bod.de
info@bod.de

Überseering 33
Hamburg
22297
Allemagne

Autres éditions populaires du même titre

9783836433129: Distance and Topology: Back to the Roots of Topology With a General Concept of Distance

Edition présentée

ISBN 10 :  3836433125 ISBN 13 :  9783836433129
Editeur : VDM Verlag Dr. Mueller E.K., 2007
Couverture souple