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Characterizations of Spherical Neighbourhoods

Published online by Cambridge University Press:  20 November 2018

C. M. Petty  and
J. M. Crotty
C. M. Petty
Affiliation:
University of Missouri, Columbia, Missouri
J. M. Crotty
Affiliation:
University of Missouri, Columbia, Missouri
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 2 , 01 April 1970 , pp. 431 - 435
Copyright
Copyright © Canadian Mathematical Society 1970

References

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