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In which metric spaces are parallel bodies of closed sets closed?

Published online by Cambridge University Press:  20 January 2009

Gerald Beer
Gerald Beer
Affiliation:
California State University, Los Angeles, Los Angeles, California 90032
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Let X be a metric space with metric d and for each x in X let Bλ[x] denote the closed ball of radius λ about x. Following Valentine [15] if K⊂X and λ is positive, then we call the set Bλ[K]=∪x∈KBλ[x] the λ-parallel body of K. The following fact is obvious.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 2 , June 1983 , pp. 265 - 273
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

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