The B-completion of a -quasi-metric space

We continue our study of the conjugate invariant method for completing an arbitrary T 0 -quasi-metric space which we have introduced in an earlier article under the name of the B-completion. We present examples that show that B-completeness of quasi-pseudometric spaces is not preserved under quasi-uniform isomorphisms. This leads to investigations of how some well-known operations applied to quasi-pseudometrics affect balancedness of their Cauchy filter pairs. We also observe that the B-completion of a totally bounded T 0 -quasi-metric space is totally bounded, but can be strictly larger than the bicompletion.