On Smital properties

摘要

Let A be an algebra and 3 C A an ideal of subsets of a group (X, +) with an invariant topology r. We say that a triple {A, ∂. τ) has the Smital property if, for any set A e A 3 and any set D dense in r, the set (A + D)~c belongs to ∂. In the paper we compare this property and similar ones with the well-known Steinhaus type properties. We consider several weak and strong versions of Smital properties.