On Cantor cubes
Н. Н. Петров · Vestnik St Petersburg University Mathematics · 2012
Some decision making models are discussed from the point of view of neurophysiology and quantum mechanics. The main feature of these models is that a straight line segment is replaced by the Cantor set. In this direction, many interesting results have been obtained by methods of number theory, p-adic analysis, and the theory of dynamical systems. Some generalizations of existing models are also discussed, which are formulated in terms of the so-called Cantor cubes, that is, Cartesian products of infinitely many standard two-point spaces D (as is known, the Cantor cube $$D^{\aleph _0 }$$ is homeomorphic to the Cantor set). This approach involves difficulties caused by the nonmetrizability and nonseparability of the Cantor cubes D m for m > ℵ0 and nonseparable for m > c, respectively.