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Hyperconvex hulls of metric spaces. (English) Zbl 0759.54015
The author’s abstract: “The following facts are shown: (1) Each bounded hyperconvex space $X$ is a hyperconvex hull of the subspace $EX$ of $X$ whose elements are the endpoints of $X$; (2) The hyperconvex hull of $R\sp n$ … with the sum metric $d\sb 1$ is $R\sp{2n-1}$ with the maximum metric $d\sb \infty$.”.

##### MSC:
 54E40 Special maps on metric spaces 54B30 Categorical methods in general topology
##### Keywords:
hyperconvex space; hyperconvex hull
Full Text:
##### References:
 [1] Aronszajn, N.; Panitchpakdi, P.: Extension of uniformly continuous transformations and hyperconvex metric spaces. Pacific J. Math. 6, 405-439 (1956) · Zbl 0074.17802 [2] Cohen, W. B.: Injective envelopes of Banach spaces. Bull amer. Math. soc. 70, 723-726 (1964) · Zbl 0124.06505 [3] Dress, A. W. M.: Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: a note on combinatorial properties of metric spaces. Adv. in math. 53, 321-402 (1984) · Zbl 0562.54041 [4] Isbell, J. R.: Six theorems about injective metric spaces. Comment. math. Helv. 39, 65-74 (1964) · Zbl 0151.30205 [5] Isbell, J. R.: Injective envelopes of Banach spaces are rigidly attached. Bull. amer. Math. soc. 70, 727-729 (1984) · Zbl 0128.34503 [6] Lacey, H. E.; Cohen, H. B.: On injective envelopes of Banach spaces. J. funct. Anal. 4, 11-30 (1969) · Zbl 0175.41802 [7] Rao, N. V.: Letter to the author. (December 1989)