Sierpinski set

Sierpinski set

[sər′pin·skē ‚set]
(mathematics)
A set of points S on a line such that both S and its complement contain at least one point in each uncountable set on the line that is a countable intersection of open sets.
A set of points in a plane that includes at least one point of each closed set of nonzero measure and does not include any subsets consisting of three collinear points.