Embedding lattice actions in flows with multidimensional time

Extensions of generic measure-preserving actions

“…Any map which respects genericity is category-preserving, and a category-preserving map respects genericity if and only if it has a dense image. Thus, in the context of this article, the two notions are essentially equivalent; compared to [20], our approach is somewhat simpler because we have Theorem 2.9 at our disposal, while [20] only uses the classical Kuratowski-Ulam theorem.…”

“…[13,14,19,20]); below we quickly discuss this approach, as well as the technique used in [15], and compare the two. Proof.…”

“…In the proof of the main result, we will also need the following facts from [15]. This criterion was applied to obtain the following result (also proved, earlier and independently, by Tikhonov [20], using his notion of map respecting genericity).…”

“…After a first draft of this paper was completed, I became aware of the paper [20], where the author considers maps which "respect genericity" -i.e. such that the inverse image of a comeager set is comeager, and the image of a comeager set is comeager.…”

“…Since then (private communication) he told me that his proof was quite different. (2) After completing a first draft of this paper, I became aware that a similar approach was used by Tikhonov [20] to study embeddings of generic actions of Z d in continuous actions of R d .…”