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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Geometric convexity. III. Embedding


Authors: John Cantwell and David C. Kay
Journal: Trans. Amer. Math. Soc. 246 (1978), 211-230
MSC: Primary 52A01
MathSciNet review: 515537
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Abstract: The straight line spaces of dimension three or higher which were considered by the first author in previous papers are shown to be isomorphic with a strongly open convex subset of a real vector space. To achieve this result we consider the classical descriptive geometry studied in various papers and textbooks by Pasch, Hilbert, Veblen, Whitehead, Coxeter, Robinson, and others, with the significant difference that the geometry considered here is not restricted to 3 dimensions. Our main theorem (which is well known in dimension 3) is that any such geometry is isomorphic to a strongly open convex subset of a real vector space whose ``chords'' play the role of lines.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0515537-7
PII: S 0002-9947(1978)0515537-7
Article copyright: © Copyright 1978 American Mathematical Society