Abstract
It is shown that each arc on a disk D in E 4 {E^4} can be homeomorphically approximated by an arc in D which is tame in E 4 {E^4} . Some applications of this are given. Also, we construct an everywhere wild ( n − 1 ) (n - 1) -sphere in E n , n ≧ 3 {E^n},n \geqq 3 , each of whose arcs is tame in E n {E^n} .
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