On paracompact [formula omitted]-subspaces of pseudocompact spaces

Abstract

Central in this article is the investigation of spaces which admit special embeddings in pseudocompact spaces. From Corollary 3.2 it follows that a paracompact space is Čech-complete provided it is a Gδ-subset of a space Y for which the Stone–Čech compactification is a dyadic space. Theorem 4.3 affirms that a paracompact p-space is a Gδ-subset of a pseudocompact space if and only if it is Čech-complete. There exist a pseudocompact space Y and its paracompact functionally closed subspace which is not a k-space (Theorem 4.6). Those subspaces do not exist in pseudocompact groups and in pseudocompact Mal'cev spaces (Corollary 3.3). A paracompact space is a closed Gδ-subspace of a pseudocompact space provided it is a Gδ-subspace of some pseudocompact space (Theorem 4.7). Some open problems are formulated.