Difference between revisions of "Dyadic discontinuum"
From Encyclopedia of Mathematics
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| − | The topological product of simple | + | {{TEX|done}} |
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| + | The [[topological product]] of simple [[colon]]s, [[discrete space]]s consisting of two points. | ||
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| − | The terminology is slightly ambiguous: a [[ | + | 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. |
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| + | 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]]). | ||
Latest revision as of 06:58, 27 April 2016
The topological product of simple colons, discrete spaces consisting of two points.
Comments
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=15910
Dyadic discontinuum. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dyadic_discontinuum&oldid=15910