Open Problem Garden - Sticky Cantor sets - Comments

M (re: Sticky Cantor sets)

Anonymous — Tue, 10 Apr 2012 20:42:52 +0200

"embedded" does not imply that it is still a subset of the line. It just says that it's one-to-one and a homeomorphism with the image. The conjecture requires to prove that there exists a Cantor which cannot be separated from itself, so showing an example where it can be separated is not relevant.

Misunderstanding (re: Sticky Cantor sets)

Anonymous — Fri, 29 Jul 2011 22:16:08 +0200

Your misunderstanding comes from the definition of a Cantor set. A Cantor set is a set homeomorphic to the usual middle-thirds Cantor set. In general it does not have to lie on a line segment.

Sticky Cantor sets

porton — Sun, 06 Feb 2011 19:26:41 +0100

Author(s):

Subject: Topology

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?