Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Distance and Topology- Back to the Roots of Topology with a General Concept of Distance

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

Heitzig, Jobst

Paperback

Business GeneralGeneral Mathematics

ISBN10: 3836433125
ISBN13: 9783836433129
Publisher: Vdm Verlag
Published: Sep 11 2007
Pages: 160
Weight: 0.58
Height: 0.34 Width: 6.69 Depth: 9.61
Language: English
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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