SPACES FOR WHICH THE FIRST UNCOUNTABLE ORDINAL SPACE IS A REMAINDER

A remainder of a locally compact, non-compact Hausdorff spaceX is anyαX − X whereαX is a Hausdorff compactification ofX. LetK(X) be the lattice of compactifications ofX. Conditions onK(X) and an internal condition are obtained which characterize when the first uncountable ordinal space is a remainder ofX.