Geodesic
On Vertical Order of One-Dimensional Compacta in E 3
Canadian journal of mathematics, Tome 36 (1984) no. 3, pp. 520-528

Voir la notice de l'article provenant de la source Cambridge University Press

Let X be a compactum in En of dimension at most n – 2. In [9, Theorem 4.1] it was shown that there is an arbitrarily small homeomorphism h of En fixed outside any given neighborhood of X, so that h(X) has vertical order n – 1 provided n ≠ 3. If X is a 0-dimensional set or a tame 1-dimensional set in E3 then the result is still true. However, the examples of tangled continua of Bothe [2] and McMillan and Row [7] are not amenable to the techniques used in dimensions other than three. This prompted Wright [9] to make the following conjecture. 
Tinsley, Fred; Wright, David G. On Vertical Order of One-Dimensional Compacta in E 3. Canadian journal of mathematics, Tome 36 (1984) no. 3, pp. 520-528. doi: 10.4153/CJM-1984-031-2
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