Abstract
A subset X X of E 3 {E^3} is said to be universally pierced if each 2 2 -sphere containing X X can be pierced by a tame arc at each point of X X . We show that an arc A A is universally pierced provided A A has a shrinking point p p such that either p p lies in a tame arc in A A or E 3 − A {E^3} - A has 1 1 -ALG at p p . Applying this result we show the existence of infinitely many wild universally pierced arcs.
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