# Polish space

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=51151