Let En be the Euclidean
n-space. A Cantor set C is a set homeomorphic with the Cantor middle-third set.
Antoine and Blankinship have shown that there exists a “wild” Cantor set in any
En for n ≧ 3, where “wild” means that En− C is not simply connected.
However it is also known that no “wild” Cantor set (in fact, compact set) can
exist in many infinite dimensional spaces, such as s (the countably infinite
product of lines) or the Hilbert space l2. A result of this paper provides a
positive answer for a generalization of Blankinship’s result in the Hilbert
cube.
