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Results tagged with descriptive-set-theory
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user 105651
Descriptive Set Theory is the study of definable subsets of Polish spaces, where definable is taken to mean from the Borel or projective hierarchies. Other topics include infinite games and determinacy, definable equivalence relations and Borel reductions between them, Polish groups, and effective descriptive set theory.
6
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Is there an almost strongly zero-dimensional space which is not strongly zero-dimensional
A Tychonoff space $X$ is called strongly zero-dimensional if each functionally closed subset $F$ of $X$ is a $C$-set, which means that $F$ is the intersection of a sequences of clopen sets in $X$.
A …
- 4,535
2
votes
0
answers
69
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Separately continuous functions of the first Baire class
Problem. Let $X,Y$ be (completely regular) topological spaces such that every separately continuous functions $f:X^2\to\mathbb R$ and $g:Y^2\to \mathbb R$ are of the first Baire class. Is every separa …
- 4,535
4
votes
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answers
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Completely I-non-measurable unions in Polish spaces
Problem. Let $X$ be a Polish space, $\mathcal I$ be a $\sigma$-ideal with Borel base, and $\mathcal A\subset\mathcal I$ be a point-finite cover of $X$. Is it true that $\mathcal A$ conatins a subfm …
- 4,535