Geodesic
Characterizations of Spherical Neighbourhoods
Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 431-435

Voir la notice de l'article provenant de la source Cambridge University Press

If Σ is a specified class of metric spaces and M ∈ Σ, then the characterization problem is to find necessary and sufficient conditions which distinguish the spherical neighbourhoods (open spheres) of M among a specified class of subsets of M.In a metric space M the notation pqr means p ≠ q ≠ r and pq + qr = pr.M is said to be uniformly locally externally convex if there exists δ > 0 such that if p, q ∈ M, p ≠ q, and pq < δ, then there exists r ∈ M such that the relation pqr subsists. We will prove the following result. 
Petty, C. M.; Crotty, J. M. Characterizations of Spherical Neighbourhoods. Canadian journal of mathematics, Tome 22 (1970) no. 2, pp. 431-435. doi: 10.4153/CJM-1970-051-9
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