A Cardinal Generalization of z-Embedding

It is known that P^κ-embedding may be viewed as a cardinal generalization of C-embedding, and that C-embedding = z-embedding + well-embedding. This chapter cardinally generalizes the notion of z-embedding to that of “z_κ-embedding” in such a way that z_ω-embedding = z-embedding, z_κ-embedding relates to P^κ-embedding in precisely the same way that z-embedding relates to C-embedding, and virtually all of the basic results concerning z-embedding generalize satisfactorily to the case of z_κ-embedding. The chapter is devoted to some technical preliminaries, including uniform discreteness, normal covers, and mappings into hedgehogs. It defines z_κ-embedding and establish some of its basic properties. The chapter is concerned with spaces in which special subsets are z_κ-embedded.