A remainder for some non-locally compact spaces

Denote by R(X) the set of points of X which have no compact neighbourhoods. If X is a non-locally compact space satisfying certain hypotheses with | R(X) | = 1, Chandler and Tzung2 proved that there exist a compactification ?X of X with ?X\X is homeomorphic to T01 = [0, 1). In this paper, we generalize this theorem