Every semitopological semigroup compactification of the group \(H_+[0,1]\) is trivial (Q5952238)

Let \(G=H_+[0, 1]\) be the topological group of all orientation-preserving selfhomeomorphisms of the closed interval \([0, 1]\) endowed with the compact-open topology. The author proves that every weakly almost periodic function on \(G\) is constant, and, consequently, every semitopological semigroup compactification of \(G\) is trivial.