Equidistant sets and their connectivity properties
HTML articles powered by AMS MathViewer
- by J. B. Wilker
- Proc. Amer. Math. Soc. 47 (1975), 446-452
- DOI: https://doi.org/10.1090/S0002-9939-1975-0355791-0
- PDF | Request permission
Abstract:
If $A$ and $B$ are nonvoid subsets of a metric space $(X,d)$, the set of points $x \in X$ for which $d(x,A) = d(x,B)$ is called the equidistant set determined by $A$ and $B$. Among other results, it is shown that if $A$ and $B$ are connected and $X$ is Euclidean $n$-space, then the equidistant set determined by $A$ and $B$ is connected.References
- H. Bell, Some topological extensions of plane geometry (manuscript).
- Morton Brown, Sets of constant distance from a planar set, Michigan Math. J. 19 (1972), 321–323. MR 315714
- Steve Ferry, When $\epsilon$-boundaries are manifolds, Fund. Math. 90 (1975/76), no. 3, 199–210. MR 413112, DOI 10.4064/fm-90-3-199-210
- Ronald Gariepy and W. D. Pepe, On the level sets of a distance function in a Minkowski space, Proc. Amer. Math. Soc. 31 (1972), 255–259. MR 287442, DOI 10.1090/S0002-9939-1972-0287442-5
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 446-452
- DOI: https://doi.org/10.1090/S0002-9939-1975-0355791-0
- MathSciNet review: 0355791