Distance and Topology

Autor:: Jobst Heitzig
Wydawnictwo:: VDM Verlag
Liczba stron:: 160
Format:: 240 mm x 170 mm x 10 mm
ISBN-13/EAN:: 9783836433129
ISBN-10:: 3836433125
Rok wydania:: wrzesień 2007 r.
Waga:: 315 g
Realizacja:: ok. 7-10 dni + wysyłka

Distance and Topology, wrzesień 2007 r. : 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.

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