In　the　third　paragraph　on　p.　2421　and　in　Theorem　1′　of　[3]　it　is　wrongly　assumed　that　“the　multiplication　on　a　topological　semigroup　T　can　be　extended　to　a　right　continuous　multiplication　on　βT”;　in　other　words,　we　wrongly　assume　that　“βT　is　a　compact　Hausdorff　right-topological　semigroup　for　any　topological　semigroup　T”.　So　using　[3,　Theorem　1]　we　can　only　obtain　the　following　two　theorems　in　place　of　[3,　Theorem　1′],　where　X′　denotes　the　limit-point　set　of　a　space　X　and　J(E)　denotes　the　set　of　all　idempotents　in　a　compact　Hausdorff　right-topological　semigroup　E.　©　2019,　Science　China　Press　and　Springer-Verlag　GmbH　Germany,　part　of　Springer　Nature.