Difference between revisions of "Polish space"
From Encyclopedia of Mathematics
(copy short text from Descriptive set theory) |
(Define Suslin space) |
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by those logicians who identify $ \mathbf N $ | by those logicians who identify $ \mathbf N $ | ||
and the first infinite [[ordinal number]] $ \omega $). | 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=51145
Polish space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polish_space&oldid=51145