On functions that preserve a certain class of sets. (English) Zbl 0706.28004

Kominek, Zygfryd; Miller, Harry I.

Boll. Unione Mat. Ital., VII. Ser., A 4, No. 2, 165-172 (1990).

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

Keywords:

additive real function; Baire set; positive Lebesgue measure