Analytic set

In descriptive set theory, a subset of a Polish space ${\displaystyle X}$ is an analytic set if it is a continuous image of a Polish space. These sets were first defined by Luzin (1917) and his student Souslin (1917).

There are several equivalent definitions of analytic set. The following conditions on a subspace A of a Polish space are equivalent:

An alternative characterization, in the specific, important, case that ${\displaystyle X}$ is Baire space ω^ω, is that the analytic sets are precisely the projections of trees on ${\displaystyle \omega \times \omega }$. Similarly, the analytic subsets of Cantor space 2^ω are precisely the projections of trees on ${\displaystyle 2\times \omega }$.

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