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Best approximation in metric spaces. (English) Zbl 0652.51019
A metric space (X,d) is called an M-space if for every x and y in X and for every $$r\in [0,\lambda]$$, where $$\lambda =d(x,y)$$, there is a $$z\in X$$ such that $$B[x,r]\cap B[y,\lambda -r]=\{z\}.$$ Also, if G is a closed subset of X and $$\rho (x,G)=\inf \{d(x,y):$$ $$y\in G\}$$, then G is called proximinal in X if the infimum is attained for all $$x\in X$$. The author studies M-spaces in terms of proximinality properties of certain sets.
Reviewer: E.J.F.Primrose

##### MSC:
 51K05 General theory of distance geometry 51K99 Distance geometry 41A50 Best approximation, Chebyshev systems
##### Keywords:
M-spaces; proximinality
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##### References:
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