Embeddings extending various types of disjoint sets (Q796852)

Characterizations of Z-embedding, C-embedding and \(C^*\)-embedding are generalized to other types of sets. For example, it is well-known that a set S is \(C^*\)-embedded in a space X if and only if two disjoint zero- sets of S can be extended to disjoint zero-sets of X. The notion of CC- embedding (obtained by replacing zero-set with cozero-set in the definition above) is introduced and studied. Other types of embedding are defined as well.