Pairwise k-semi-stratifiable bispaces and topological ordered spaces

In this paper, we continue to study pairwise (k-semi-)stratifiable bitopological spaces. Some new characterizations of pairwise k-semi-stratifiable bitopological spaces are provided. Relationships between pairwise stratifiable and pairwise k-semi-stratifiable bitopological spaces are further investigated, and an open question recently posed by Li and Lin in [18] is completely solved. We also study the quasi-pseudo-metrizability of a topological ordered space (X,τ,≼). It is shown that if (X,τ,≼) is a ball transitive topological ordered C- and I-space such that τ is metrizable, then its associated bitopological space (X,τ♭,τ♮) is quasi-pseudo-metrizable. This result provides a partial affirmative answer to a problem in [15].