Uniqueness of spaces pretangent to metric spaces at infinity
Keyword(s):
We find the necessary and sufficient conditions under which an unbounded metric space \(X\) has, at infinity, a unique pretangent space \(\Omega^{X}_{\infty,\tilde{r}}\) for every scaling sequence \(\tilde{r}\). In particular, it is proved that \(\Omega^{X}_{\infty,\tilde{r}}\) is unique and isometric to the closure of \(X\) for every logarithmic spiral \(X\) and every \(\tilde{r}\). It is also shown that the uniqueness of pretangent spaces to subsets of a real line is closely related to the ''asymptotic asymmetry'' of these subsets.
1970 ◽
Vol 22
(2)
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pp. 431-435
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2020 ◽
Vol 30
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pp. 2050030
1994 ◽
Vol 17
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pp. 713-716
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2000 ◽
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pp. 773-779
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pp. 177-205
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2001 ◽
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pp. 391-397
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