The fundamental concept with which we shall be concerned throughout this book is that of distance. We shall explore the geometry of spaces whose distance functions possess various properties that compare favourably to those of the distance function in Euclidean space. If such properties are identified and articulated clearly, then by proceeding in simple steps from these defining properties one can recover much of the elegant structure of classical geometry, now adapted to a wider context.
KeywordsTriangle Inequality Cayley Graph Geodesic Segment Geodesic Path Normed Vector Space
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