Embedding and immersion numbers of manifolds with boundary (Q1262584)

In his paper ``On embedding numbers of differentiable manifolds'' [Topology 7, 95-109 (1968; Zbl 0152.408)], \textit{I. Berstein} investigated the embedding numbers of a closed manifold V. He defined the embedding number of V in codimension k to be the least possible number of open subsets that embed in codimension k each, and together cover V. The author of the paper under review generalizes this concept to manifolds with boundary and proves some elementary properties of it and of an analogously defined immersion covering number. Furthermore, he obtains an inequality for the covering numbers of a product of two manifolds.