Cantorternary Set

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Cantorternary Set

 

a perfect set of points on a line that does not contain a single interval; it was constructed by G. Cantor in 1883. It is obtained by first removing the middle third (1/3, 2/3) from the closed interval [0, 1], then removing the middle thirds (1/9, 2/9) and (7/9, 8/9) of the remaining closed intervals[0, 1/3] and [2/3, 1], and so on. The Cantor ternary set has the power of the continuum. The set may be defined arithmetically as the totality of ternary fractions 0. a1an …, where each of the digits a, 1a2, …, an, … is 0 or 2. The Cantor ternary set plays an important role in various problems of mathematics (in topology and in the theory of functions of a real variable).

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.