More about complements of quasi-uniformities

We continue our investigations on the lattice ( q ( X ) , ⊆ ) of quasi-uniformities on a set X. Improving on earlier results, we show that the Pervin quasi-uniformity (resp. the well-monotone quasi-uniformity) of an infinite topological T 1 -space X does not have a complement in ( q ( X ) , ⊆ ) . We also establish that a hereditarily precompact quasi-uniformity inducing the discrete topology on an infinite set X does not have a complement in ( q ( X ) , ⊆ ) .