A Cantor set 
in 
is said to be scrawny if for each neighborhood 
of an arbitrary point 
in 
, there is a neighborhood 
of 
such that every map 
extends to a map 
such that 
is finite. Babich (1992) presents examples of wild
Cantor sets of this type and provides a proof that such objects cannot be defined
by solid tori.
Scrawny Cantor Set
See also
Cantor SetExplore with Wolfram|Alpha
References
Babich, A. "Scrawny Cantor Sets are Not Definable by Tori." Proc. Amer. Math. Soc. 115, 829-836, 1992.Referenced on Wolfram|Alpha
Scrawny Cantor SetCite this as:
Weisstein, Eric W. "Scrawny Cantor Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ScrawnyCantorSet.html