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Difference between revisions of "Dyadic discontinuum"

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The topological product of simple colons, discrete spaces consisting of two points.
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The [[topological product]] of simple [[colon]]s, [[discrete space]]s consisting of two points.
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====Comments====
 
====Comments====
Such products are also called Cantor cubes; they topologically contain every [[Zero-dimensional space|zero-dimensional space]]. Also, every [[Compact space|compact space]] is the continuous image of a closed subspace of a Cantor cube.
 
  
The terminology is slightly ambiguous: a [[Dyadic space|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|Totally-disconnected space]]).
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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.
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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