Countable compactifications of topological spaces have been studied in [1], [5], [7], and [9]. In [7], Magill showed that a locally compact, T2 topological space X has a countable T2 compactification if and only if it has n-point T2 compactifications for every integer n ≥ 1. We generalize this theorem to T2-ordered compactifications of ordered topological spaces. Before starting our generalizat...

In this note we study the dynamics of the natural evaluation action of the group of isometries G of a locally compact metric space (X, d) with one end. Using the notion of pseudocomponents introduced by S. Gao and A. S. Kechris we show that X has only finitely many pseudo-components exactly one of which is not compact andG acts properly on this pseudo-component. The complement of the non-compac...

We derive major parts of the eigenvalue spectrum operators on squashed seven-sphere that appear in compactification eleven-dimensional supergravity. These spectra determine mass fields $AdS_4$ and are important for corresponding ${\mathcal N} =1$ supermultiplet structure. This work is a continuation [1] where complete irreducible isometry representations was derived this compactification. Some ...