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An Axiomatic Line Geometry

Published online by Cambridge University Press:  20 November 2018

Stanton Trott
Stanton Trott*
Affiliation:
University of Toronto, Toronto, Ontario
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In their classic treatment (5) Veblen and Young build n-dimensional projective geometry from points and lines. Naturally, each line becomes identified with the set of points with which it is incident, and many treatments build from points alone, postulating the existence of certain distinguished subsets of the set of points. From either point of view, some labour is required, even in the two-dimensional case, to establish duality; hence a considerable interest attaches to self-dual systems of axioms; cf. (2; 3).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 20 , 1968 , pp. 939 - 952
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Coxeter, H. S. M., Projective line geometry, Math. Notae 1 (1962), 197–216.Google Scholar
2. Esser, M., Self-dual postulates for n-dimensional projective geometry, Duke Math. J. 18 1951), 475–480.Google Scholar
3. Menger, K., The projective space, Duke Math. J. 17 (1950), 1–14.Google Scholar
4. Segre, B., Lectures on modern geometry (Cremorne, Rome, 1961).Google Scholar
5. Veblen, O. and Young, J. W., Projective geometry, Vol. I (Ginn, Boston, 1910).Google Scholar