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A fundamental theorem for dimension-free Möbius sphere geometries
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- Autor/in:
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- Erscheinungsjahr:
- 2008
- Medientyp:
- Text
- Schlagworte:
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- Dimension-free geometry
- Functional equation
- Isomorphism of geometries
- Möbius geometry of arbitrary (finite or infinite) dimension
- Real inner product space
- Beschreibung:
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- Let (X, δ) and (V, ε) be real inner product spaces of (finite or infinite) dimensions dim X, dim V greater than 1 (see our book [1] for special notions, results and the notation applied in the present paper). Especially the following Theorem 2 will be proved. The Möbius sphere geometries (X ∪ {∞}, double-struck M(X,δ)), (V ∪ {∞}, double-struck M(V,ε)) over (X,δ), (V,ε), respectively, where double-struck M is the Möbius group, are isomorphic (see [1], p. 16 f) if, and only if, (X,δ) ≅ (V,ε) (see [1], p. 1 f). © 2008 Birkhäuser Verlag AG.
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- info:eu-repo/semantics/closedAccess
- Quellsystem:
- Forschungsinformationssystem der UHH
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- oai:www.edit.fis.uni-hamburg.de:publications/cd1a43c2-f989-49b3-8b4c-737a798c20ba