**Conjecture**Let be a Cantor set embedded in . Is there a self-homeomorphism of for every greater than so that moves every point by less than and does not intersect ? Such an embedded Cantor set for which no such exists (for some ) is called "sticky". For what dimensions do sticky Cantor sets exist?

I borrowed this conjecture from this forum thread.

Certainly I understand this conjecture wrongly: is a subset of a line segment. Consider a homeomorphism which moves all points of orthogonally to this line segment by . This would be a solution of this problem. Obviously it is not what is meant.

Indeed I submit the problem to OPG as is in the hope that somebody will correct my wrong understanding and adjust the formulation to not be misunderstood as by me.

## Bibliography

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