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Difference between revisions of "Polish space"

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(Define Suslin space)
 
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A [[Separable space|separable]] [[topologically complete space]].  See [[Descriptive set theory]].
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A [[Separable space|separable]] [[topologically complete space]].  Polish spaces form a natural frame of [[descriptive set theory]]. The fundamental Polish space  $  \mathbf I $
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of irrationals is homeomorphic to the [[Baire space]]  $  \mathbf N  ^ {\mathbf N} $(
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often denoted by  $  \omega  ^  \omega  $
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by those logicians who identify  $  \mathbf N $
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and the first infinite [[ordinal number]]  $  \omega $).
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A '''Suslin space''' is a continuous image of a Polish space.

Latest revision as of 19:36, 1 January 2021

A separable topologically complete space. Polish spaces form a natural frame of descriptive set theory. The fundamental Polish space $ \mathbf I $ of irrationals is homeomorphic to the Baire space $ \mathbf N ^ {\mathbf N} $( often denoted by $ \omega ^ \omega $ by those logicians who identify $ \mathbf N $ and the first infinite ordinal number $ \omega $).

A Suslin space is a continuous image of a Polish space.

How to Cite This Entry:
Polish space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polish_space&oldid=51140