Compact condensations and compactifications

摘要

A Tychonoff space X will be called strongly bicompactly condensable (SBC) if there is a set S of compact Hausdorff topologies on the set X whose supremum in the lattice of topologies is the original topology. Such an S determines a compactification K(S) of X. We examine which compactifications of an SBC X arise in this way: For some X, all do, and for others, some and not all; For some X, beta X does, and for others, does not. (C) 2019 Elsevier B.V. All rights reserved.