Bicompletion and Samuel Bicompactification

It is proved that the quasi-proximity space induced by the bicompletion of a quasi-uniform T0-space X is a subspace of the quasi-proximity space induced by the Samuel bicompactification of X. The result is then used to establish that the locally finite covering quasi-uniformity defined on the category Top0 of topological T0-spaces and continuous maps is not lower K-true (in the sense of Brümmer). It is also shown that a functorial quasi-uniformity F on Top0 is upper K-true if and only if FX is bicomplete whenever X is sober.