×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite