Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-21T22:27:45.308Z Has data issue: false hasContentIssue false

A Characterization of Line Spaces

Published online by Cambridge University Press:  20 November 2018

J. H. M. Whitfield
Affiliation:
Lakehead UniversityThunder Bay, Ontario
S. Yong
Affiliation:
Lakehead UniversityThunder Bay, Ontario
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
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