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On the Steiner Problem

Published online by Cambridge University Press:  20 November 2018

E. J. Cockayne
E. J. Cockayne*
Affiliation:
University of Victoria
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Let M be a metric space with metric ρ which has the following properties.

1. M is finitely compact.

2. There exists a geodesic in M joining each two points of M.

3. For all a, b∈M, ρ(a, b) is equal to the length of a geodesic joining a and b.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 3 , August 1967 , pp. 431 - 450
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Melzak, Z. A., On the Problem of Steiner. Canadian Mathematical Bulletin. Vol. 4,(1966), pp. 143-148.Google Scholar
2. Courant, R. and Robbins, H., What is Mathematics? (New York 1941).Google Scholar
3. Prim, R. C., Shortest Connecting Networks. Bell System Tech. Journal 31, pp. 1398-1401.Google Scholar
4. Wetherburn, C. E., Differential Geometry of Three Dimensions. (Cambridge 1947).Google Scholar
5. Blumenthal, L. M., Theory and Applications of Distance Geometry. (Oxford 1953).Google Scholar
6. Hanan, M., On the Steiner Problem with Rectilinear Distance. S. I. A. M. Journal of Applied Mathematics. vol. 14 (1966), pp. Z55-265.Google Scholar