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Dyadic discontinuum

From Encyclopedia of Mathematics
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The topological product of simple colons, discrete spaces consisting of two points.

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Such products are also called Cantor cubes; they topologically contain every zero-dimensional space. Also, every compact space is the continuous image of a closed subspace of a Cantor cube.

The terminology is slightly ambiguous: a dyadic space is a continuous image of a Cantor cube, so that "dyadic discontinuum" could also mean "totally-disconnected dyadic space" (cf. Totally-disconnected space).

How to Cite This Entry:
Dyadic discontinuum. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dyadic_discontinuum&oldid=38662