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.
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About the Author
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.
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Distance and Topology
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 164 pp. Englisch. Seller Inventory # 9783639450446
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Distance and Topology
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Autor/Autorin: Heitzig JobstThe 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 liv. Seller Inventory # 4989240
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Distance and Topology
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Distance and Topology
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Distance and Topology
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.VDM Verlag, Dudweiler Landstraße 99, 66123 Saarbrücken 164 pp. Englisch. Seller Inventory # 9783639450446
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Distance and Topology | Back to the Roots of Topology with a General Concept of Distance
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Taschenbuch. Condition: Neu. Distance and Topology | Back to the Roots of Topology with a General Concept of Distance | Jobst Heitzig | Taschenbuch | 164 S. | Englisch | 2014 | AV Akademikerverlag | EAN 9783639450446 | Verantwortliche Person für die EU: BoD - Books on Demand, In de Tarpen 42, 22848 Norderstedt, info[at]bod[dot]de | Anbieter: preigu. Seller Inventory # 106333161
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Taschenbuch. Condition: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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. Seller Inventory # 9783639450446
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