A compactification problem of J. de Groot (Q1065420)

The authors consider the notions of compactness degree (cmp X), compactness deficiency (def X), large inductive compactness degree (Cmp X), and another invariant due to E. Sklyarenko (Skl X), related to (recently disproved) conjecture of J. de Groot: cmp X\(=def X\) for every (separable metric) space. They prove the inequality Cmp \(X\leq Skl X\) for any separable metric space X, and offer an upper bound for def X: if \(X=A\cup B\), where X is a separable metric space, A is closed and B is locally compact, then def \(X\leq \dim A+1\).