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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-9, author = {Yuji Akaike and Naotsugu Chinen and Kazuo Tomoyasu}, title = {Perfectness of the Higson and Smirnov compactifications}, journal = {Colloquium Mathematicae}, volume = {107}, year = {2007}, pages = {89-98}, zbl = {1118.54013}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-9} }
Yuji Akaike; Naotsugu Chinen; Kazuo Tomoyasu. Perfectness of the Higson and Smirnov compactifications. Colloquium Mathematicae, Tome 107 (2007) pp. 89-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm107-1-9/