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On functions that preserve a certain class of sets. (English) Zbl 0706.28004
The authors study the set $${\mathcal A}$$ defined as follows: a subset B of R belongs to $${\mathcal A}$$ if $$D(B)=\{a-b| \quad a,b\in B\}$$ contains a non-empty open interval. It is shown that $${\mathcal A}$$ has minimal members under inclusion. Other questions on functions from R into R which preserve (or do not preserve) the set $${\mathcal A}$$ are considered.
Reviewer: O.T.Alas

##### MSC:
 28A05 Classes of sets (Borel fields, $$\sigma$$-rings, etc.), measurable sets, Suslin sets, analytic sets