The decomposable and the ambiguous sets

O. Karlova


We prove that every ambiguous subset of a hereditarily Baire space is decomposable. We obtain that a decomposable set $ A \subseteq X$ is ambiguous when (i) $X$ is a perfectly paracompactspace, or (ii) $A$ and $X \setminus A$ are Lindelöf and $X$ is a completely regular space.

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