Spaces for which the first uncountable ordinal space is a remainder (Q1087176)

A remainder of a locally compact, non-compact Hausdorff space X is any \(\alpha\) X-X, where \(\alpha\) X is a Hausdorff compactification of X. Let K(X) be the lattice of compactifications of X. Conditions on K(X) and an internal condition are obtained which characterize when the first uncountable ordinal space is a remainder of X.