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

Jobst Heitzig

 
9783836433129: Distance and Topology- Back to the Roots of Topology with a General Concept of Distance
Tapa blanda
ISBN 10: 3836433125 ISBN 13: 9783836433129
Editorial: KS OmniScriptum Publishing, 2007

Sinopsis

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 make more specific contributions to distancetheory.We start by learning the basic properties of distance, endowing all kinds ofmathematical objects with a distance function, and studying interesting kindsof mappings between such objects. This leads to new characterizations ofmany well-known types of mappings. Then a suitable notion of distancespaces is developed, general enough to induce most topological structures,and we study topological properties of mappings like the concept of stronguniform continuity.Important results include a new characterization of the similarity mapsbetween Euclidean spaces, and generalizations of completion methods andfixed point theorems, most notably of the famous one by Brouwer. We closewith a short study of distance visualization techniques.

"Sinopsis" puede pertenecer a otra edición de este libro.

Reseña del editor

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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
KS OmniScriptum Publishing
Año de publicación
2007
Idioma
Inglés
ISBN 10 
3836433125
ISBN 13 
9783836433129
Encuadernación
Tapa blanda
Número de páginas
160
Contacto del fabricante
no disponible
Persona responsable
no disponible