Every semitopological semigroup compactification of the group H+[0,1] is trivial

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Embedding the bicyclic semigroup into countably compact topological semigroups (2008, background): “It follows that c = xy ∈ O(a)·O(b) ⊂ S\{c} which is a contradiction.”
Automatic continuity of homomorphisms and fixed points on metric compacta (2006, background): “Megrelishvili [14], proving a conjecture of Pestov, has shown that Homeo+(R) has no non-trivial strongly continuous representations by linear isometries on a reflexive Banach space.”