Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Convex metric spaces with 0-dimensional midsets


Authors: L. D. Loveland and J. E. Valentine
Journal: Proc. Amer. Math. Soc. 37 (1973), 568-571
MSC: Primary 53C70; Secondary 52A50
MathSciNet review: 0310817
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let X be a nontrivial, complete, convex, locally externally convex metric space. Assuming that the midset of each pair of points of X is 0-dimensional and that any nonmaximal metric segment that intersects a midset twice lies in that midset, we show that X is isometric to either the euclidean line $ {E^1}$ or to a 1-dimensional spherical space $ {S_{1,\alpha }}$ (the circle of radius $ \alpha $ in the euclidean plane with the ``shorter arc'' metric).


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 53C70, 52A50

Retrieve articles in all journals with MSC: 53C70, 52A50


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0310817-3
Keywords: Convex, locally externally convex, midsets, weak linear midset property, 0-dimensional midsets
Article copyright: © Copyright 1973 American Mathematical Society