The category of compactifications and its coreflections

[摘要] We define ``the category of compactifications", which is denoted {\bf{CM}}, and consider its family of coreflections, denoted {\bf{corCM}}. We show that {\bf{corCM}} is a complete lattice with bottom the identity and top an interpretation of the Čech-Stone \beta. A c \in{\bf{corCM}} implies the assignment to each locally compact, noncompact Y a compactification minimum for membership in the ``object-range" of c. We describe the minimum proper compactifications of locally compact, noncompact spaces, show that these generate the atoms in {\bf{corCM}} (thus {\bf{corCM}} is not a set), show that any c \in{\bf{corCM}} not the identity is above an atom, and that \beta is not the supremum of atoms.

[学科分类] 物理化学和理论化学

[关键词] compactification;coreflection;atom in a lattice