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Results tagged with descriptive-set-theory
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user 43954
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.
5
votes
sets without perfect subset in a non-separable completely metrizable space
[2]$\Rightarrow$ [1]. It is easy to check that each discrete subset $D’$ of a perfect space $P$ is nowhere dense in $P$. Now suppose that $D$ is a countable union of discrete subsets of $X$ and $D$ c …
- 5,409
11
votes
Accepted
Non meager rectangle
I pointed this question to Taras Banakh,
who pointed to me his joint paper with Lyubomyr Zdomskyy “Non-meager free sets for meager relations on Polish spaces” which contains an answer.
Abstract. We …
- 5,409
3
votes
Accepted
Does a continuous map from $\kappa^\omega$ to $[0,1]^\omega$ have a non-scattered fiber?
The continuity of $f$ is not needed. Indeed, suppose to the contrary that $\kappa^\omega$ is a union of the family $\{F_\alpha:\alpha<\frak c\}$ of fibers of $f$. Let $\alpha<\frak c$ be any index. Si …
- 5,409
6
votes
1
answer
293
views
A rather non-$F_\sigma$ Borel set
I asked this question at MSE a week ago, but received no answer, so I cross-post it here.
I obtained a negative answer to this MSE question provided each metric space $X$ such that $|X|=\frak c$ and d …
- 5,409