What is a Cantor set?
(Thanks to Pavel Pokorny for contributing to this answer) A Cantor set is a surprising set of points that is both infinite (uncountably so, see [2.14]) and yet diffuse. It is a simple example of a fractal, and occurs, for example as the strange repellor in the logistic map (see [2.15]) when r>4. The standard example of a Cantor set is the “middle thirds” set constructed on the interval between 0 and 1. First, remove the middle third. Two intervals remain, each one of length one third. From each remaining interval remove the middle third. Repeat the last step infinitely many times. What remains is a Cantor set. More generally (and abstrusely) a Cantor set is defined topologically as a nonempty, compact set which is perfect (every point is a limit point) and totally disconnected (every pair of points in the set are contained in disjoint covering neighborhoods). See also • http://www.shu.edu/html/teaching/math/reals/topo/defs/cantor.html • http://personal.bgsu.edu/~carother/cantor/Cantor1
