A bitopological view of quasi-topological groups

A quasi-bitopological group is a triple (G, T, T-1) such that (G, T) is a quasi-topological group and T-1 is the conjugate topology of T, i.e., T-1 = {A subset of or equal to G:A(-1) is an element of T}. We prove, among other results, the following : (1) Each quasi-bitopological group is quasi-uniformizable; (2) Each first countable quasi-bitopological group admits a compatible left invariant quasi-pseudometric; (3) If (G, T, T-1) is a 2-Hausdorff quasi-bitopological group, there is a 2-Hausdorff quasi-bitopological group which is bicomplete in its two-sided quasi-uniformity and has G as a 2-dense quasi-bitopological subgroup.