Normal embeddings are characterized in terms of an approximate extension property, whence a generalization of certain cofibration properties to normal embeddings in the context of strong shape is deduced. Statements of Mayer-Vietoris type and a description of inclusion maps, which are invertible in the strong shape category, are presented as examples.

We study a condition that allows us to characterize all real hypersurfaces of quaternionic projective space known until now.

P. Borst introduced a transfinite extension of the covering dimension. In this paper we obtain compactification and factorization theorems for this dimension function.

A characterization is given of integral domains $R$ such that $R$ is a finitely generated $S$-module for each subring $S$ of $R$ which has the same quotient field as $R$. Apart from the absolutely algebraic fields of positive characteristic, such $R$ are subrings of the rings of integers of certain global fields.