Compactifications

Abstract

Every completely regular space has at least one Hausdorff compactification and much research in Topology has been devoted to methods of constructing the compactifications of completely regular spaces. These methods fall into two general categories: internal methods and external methods. External methods are characterized by their reliance on structures which are not topological or outside the immediate topological structure of the space in question; examples of the former are A. Weil [20] - uniform structures and Yu. Smirnov [15] who uses the proximity structures of Efremovich; using the continuous real-valued functions to produce an embedding of the space serves as an example of the latter.