Difference between revisions of "Polish space"
From Encyclopedia of Mathematics
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| − | A [[Separable space|separable]] [[topologically complete space]]. | + | A [[Separable space|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 $). | ||
Revision as of 19:26, 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 $).
How to Cite This Entry:
Polish space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polish_space&oldid=51145
Polish space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polish_space&oldid=51145