Perfectness of the Higson and Smirnov compactifications
Colloquium Mathematicum 107 (2007), 89-98 MSC: Primary 54D05, 54D35; Secondary 54D40, 54D45. DOI: 10.4064/cm107-1-9
We provide a necessary and sufficient condition for the Higson compactification to be perfect for the noncompact, locally connected, proper metric spaces. We also discuss perfectness of the Smirnov compactification.