Sur l’axiomatique des espaces à convexité

Abstract

In this note we compare the axiomatic of the spaces with convexity in the sense of V.W. Bryant and R.J. Webster [3], [4], [5] to the axiomatic of the (plane) geometry after Hilbert.
We find that the system of axioms of the spaces with convexity is the adaptation to the infinite dimensional case of the system formed by the first two groups of axioms: of incidence and of order. The spaces with convexity may be regarded as infinite dimensional non-Euclidean spaces.

Authors

Radu Precup
Faculty of Mathematics, Babeş-Bolyai University, Cluj-Napoca, Romania

English title

On the axiomatic of spaces with convexity

Keywords

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Cite this paper as:

R. Precup, Sur l’axiomatique des espaces à convexité, Rev. Anal. Numer. Theor. Approx., 9 (1980) no. 2, pp. 95-103.

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Journal

Revue d`analyse numérique et de théorie d`approximation

Publisher Name

Academia Republicii S.R.

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MR: 83c:52003.

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References

[1] Barbilian, D., Opera didactică, vol. III, Ed. Tehnică, Bucureşti, 1976.

[2] Bryant, Victor, Independent axioms for convexity. J. Geometry 5 (1974), 95-99, MR0355820, https://doi.org/10.1007/bf01954539

[3] Bryant, V. W., Webster, R. J., Convexity spaces. I. The basic properties. J. Math. Anal. Appl. 37 (1972), 206-213, MR0296812, https://doi.org/10.1016/0022-247x(72)90268-5

[4] Bryant, V. W., Webster, R. J., Convexity spaces. II. Separation. J. Math. Anal. Appl. 43 (1973), 321-327, MR0380622, https://doi.org/10.1016/0022-247x(73)90076-0

[5] Bryant, V. W., Webster, R. J., Convexity spaces. III. Dimension. J. Math. Anal. Appl. 57 (1977), no. 2, 382-392, MR0467541.

[6] Ghika, Al, Séparation des ensembles convexes dans les espaces lignés non vectoriels. (Romanian) Acad. Repub. Pop. Romîne. Bul. Şti. Secţ. Şti. Mat. Fiz. 7 (1955), 287-296, MR0074011.

[7] Prenowitz, Walter, A contemporary approach to classical geometry. Amer. Math. Monthly 68 1961 no. 1, part II, v+67 pp., MR0123931.

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