Locally compact spaces whose Alexandroff one-point compactifications are perfect

Perfectness of the Higson and Smirnov compactifications

“…Furthermore, it is known that the one-point compactifica-tion of the n-dimensional Euclidean space R n is perfect if and only if n > 1 (cf. [5]). …”

Conditions under which the least compactification of a regular continuous frame is perfect

“…The motivation for investigating this problem comes from the work of Jung [5] who considered this problem in the setting of Hausdorff spaces. Specifically he was concerned with characterizing internally those locally compact Hausdorff spaces whose Alexandroff one-point compactifications are perfect.…”