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A generalized Mazurkiewicz-Sierpiński theorem with an application to analytic sets. (English) Zbl 0645.54031
S. Mazurkiewicz and W. Sierpinski [Fundam. Math. 6, 161-169 (1924)] showed that if A is an analytic subset of a product of two Polish spaces then the set of first coordinates of uncountable vertical sections is analytic. The autor proves the following higher-dimensional analogue: if A is an analytic subset of the Polish space $$X\times Y\times Z$$ then $$\{$$ $$x\in X:$$ A(x) is not reticulate in $$Y\times Z\}$$ is analytic. Here, A(x) is the “two-dimensional” vertical section over x, and a subset of $$Y\times Z$$ is reticulate if it is covered by countably many of its horizontal and vertical sections.
Reviewer: F.van Engelen
##### MSC:
 54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets) 03E15 Descriptive set theory
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