Resumen de One-point order-compactifications

Guram Bezhanishvili, Patrick J. Morandi

• We classify all one-point order-compactifications of a noncompact locally compact order-Hausdorff ordered topological space X. We give a necessary and sufficient condition for a one-point order-compactification of X to be a Priestley space. We show that although among the one-point order-compactifications of X there may not be a least one, there always is a largest one, which coincides with the one-point order-compactification of McCallion. In fact, we prove that whenever X satisfies the condition given in McCartan, then the largest one-point order-compactification of X coincides with the one described by McCartan.