Left-topological semigroup
= Left-topological semigroup
A <left-topological semigroup> is a <semigroup> with a <topology> for which every left translation $L_a:x\mapsto ax$ is a <continuous map>. Here $a$ is fixed and the right input varies. Requiring continuous right translations $R_a:x\mapsto xa$ instead gives a <right-topological semigroup>.<Ergodic Ramsey Theory - an update by Vitaly Bergelson>[§3, Theorem 3.3, p. 28: left-topological means continuity of x↦ax]{ref}