Cantor dust, named after the mathematician Georg Cantor, is the two-dimensional version of the Cantor set.
In the limit, starting from a square the construction produces a set with an infinite number of square sections each having zero area — the sum of all areas also decreases to zero in the limit.
In 1911, Cantor was one of the distinguished foreign scholars invited to attend the 500th anniversary of the founding of the University of St. Andrews in Scotland.
For Kronecker, Cantor's hierarchy of infinities was inadmissible.
Cantor was the first to formulate what later came to be known as the continuum hypothesis or CH: there exists no set whose power is greater than that of the naturals and less than that of the reals (or equivalently, the cardinality of the reals is exactly aleph-one, rather than just at least aleph-one).
Since the Cantor set is the complement of a union of open sets, it itself is a closed subset of the reals, and therefore a complete metric space.
The Cantor set is a homogeneous space in the sense that for any two points x and y in the Cantor set C, there exists a homeomorphism f : C → C with f(x) = y.
Cantor himself was led to it by practical concerns about the set of points where a trigonometric series might fail to converge.
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