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A Characterization of Line Spaces

Published online by Cambridge University Press:  20 November 2018

J. H. M. Whitfield  and
S. Yong
J. H. M. Whitfield
Affiliation:
Lakehead UniversityThunder Bay, Ontario
S. Yong
Affiliation:
Lakehead UniversityThunder Bay, Ontario
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Abstract

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The line spaces of J. Cantwell are characterized among the axiomatic convexity spaces defined by Kay and Womble. This characterization is coupled with a recent result of Doignon to give an intrinsic solution of the linearization problem.

Keywords

52A0550D15Convexity spaceline spacelinearization.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 24 , Issue 3 , 01 September 1981 , pp. 273 - 277
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Birkhoff, G., Lattice Theory (3rd ed.) Providence, Rhode Island, Amer. Math. Soc, 1967.Google Scholar
2. Bryant, V. W., Independent axioms for convexity, J. Geometr. 5 (1974), 95-99.Google Scholar
3. Cantwell, J., Geometric convexity. L, Bull. Inst. Math. Acad. Sinic. 2 (1974), 289-307.Google Scholar
4. Cantwell, J. and Kay, D. C., Geometric convexity. III., Embedding., Trans. Amer. Math. Soc. 246 (1978), 211-230.Google Scholar
5. Coxeter, H. S. M., Introduction to Geometry, New York, John Wiley and Sons, 1969.Google Scholar
6. Doignon, J.-P., Caractérisations d'espaces de Pasch-Peano, Bull, de l'acad. royale de Belgique (Class des Sciences). 62 (1976), 679-699.Google Scholar
7. Kay, D. C. and Womble, E. W., Axiomatic convexity theory and relationships between the Caratheodory, Helly and Radon numbers, Pacific J. Math. 38 (1971), 471-485.Google Scholar
8. Mah, P., Naimpally, S. A., and Whitfield, J. H. M., Linearization of a convexity space, J. London Math. Soc. (2). 13 (1976), 209-214.Google Scholar
9. Szafran, D. A. and Weston, J. H., An internal solution to the problem of linearization of a convexity space, Canad. Math. Bull. 19 (1976), 487-494.Google Scholar