Mapping Cylinders and Compact Monoids.
We prove that a separable Hausdor_ topological space X containing a cocountable subset homeomorphic to [0, ω1] admits no separately continuous mean operation and no diagonally continuous n-mean for n ≥ 2.
Generalizing the notion of matched pair of groups, we define and study matched pairs of locally compact groupoids endowed with Haar systems, in order to give new examples of measured quantum groupoids.