Compactifying topologised semigroups (Q1206794)

In this note the author constructs to every semigroup \(S\) which is endowed with a topology \(\tau\) (no continuity of left or right translations assumed) the unique semitopological reflection, i.e., a semitopological semigroup \(\sigma S\), together with a continuous homomorphism \(\sigma: S \to \sigma S\) such that every continuous homomorphism \(f: S \to T\) into a semitopological semigroup \(T\) factors over \(\sigma\).