Semilattices of totally bounded quasi-uniformities (Q5939249)

The authors show that the set of all totally bounded quasi-uniformities compatible with a given topology does not have good lattice-theoretic properties. For example, even if this set is a lattice, it need not be modular. They also prove that for every nonzero cardinal \(\kappa\), there exists a topological space that admits exactly \(\kappa\) totally bounded quasi-uniformities.