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

Heitzig, Jobst

 
9783836433129: Distance and Topology: Back to the Roots of Topology With a General Concept of Distance
Brossura
ISBN 10: 3836433125 ISBN 13: 9783836433129
Casa editrice: Vdm Verlag Dr Mueller E K, 2007

Sinossi

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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Editore
Vdm Verlag Dr Mueller E K
Data di pubblicazione
2007
Lingua
Inglese
ISBN 10 
3836433125
ISBN 13 
9783836433129
Rilegatura
Copertina flessibile
Numero di pagine
160
Contatto del produttore
non disponibile
Persona responsabile
non disponibile

Altre edizioni note dello stesso titolo

9783639450446: Distance and Topology: Back to the Roots of Topology with a General Concept of Distance

Edizione in evidenza

ISBN 10:  3639450442 ISBN 13:  9783639450446
Casa editrice: AV Akademikerverlag, 2012
Brossura