Difference between revisions of "Polish space"
From Encyclopedia of Mathematics
m (ce) |
(Define Suslin space) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 1: | Line 1: | ||
| − | 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 $). | ||
| + | |||
| + | 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
Polish space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Polish_space&oldid=51140