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Geometry pp 272-343 | Cite as

The Theory of Isometries

  • Richard S. Millman
  • George D. Parker
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

In mathematics when we have a class of objects satisfying certain axioms (such as incidence geometries) it is natural to study functions that send one object to another. Such functions are most interesting when they preserve special properties of the objects. If G = {I,ℒ,d} and G′ = {I′,ℒ′,d′} are metric geometries and if ϕ:II′; is a function, what geometric properties could we reasonably require ϕ to have?

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Copyright information

© Springer-Verlag Inc. 1981

Authors and Affiliations

  • Richard S. Millman
    • 1
  • George D. Parker
    • 2
  1. 1.Department of Mathematical and Computer ScienceMichigan Technological UniversityHoughtonUSA
  2. 2.Department of MathematicsSouthern Illinois UniversityCarbondaleUSA

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