On pairwise k-semi-stratifiable spaces

Pairwise k-semi-stratifiable bispaces and topological ordered spaces

“…Recently, Li and Lin [18] introduced the concept of a pairwise k-semi-stratifiable bispace, which is a natural extension of a k-semi-straitifiable space introduced in [19] to the setting of bispaces. For i, j = 1, 2 with i = j, a bispace (X, τ 1 , τ 2 ) is called τ ik-semi-stratifiable with respect to τ j if there exists an operator G ij : [18] if it is both τ 1 -k-semistratifiable with respect to τ 2 and τ 2 -k-semi-stratifiable with respect to τ 1 .…”

“…In [18], Li and Lin characterized pairwise k-semi-stratifiable bispaces in terms of pairwise g-functions and extensions of semi-continuous functions. In this section, we continue to investigate how to characterize pairwise k-semi-stratifiable bispaces.…”

“…In this section, we continue to investigate how to characterize pairwise k-semi-stratifiable bispaces. Our first two results can be regarded as either improvements or extensions of a theorem in [18]. In addition, we also use cushioned pair k-networks and cs-networks to characterize pairwise k-semi-stratifiable bispaces.…”

“…In a recent paper [18], Li and Lin posed the following open question (see [18,Question 3.4]). Our next theorem answers Question 4.1 affirmatively.…”

“…In Section 4, we consider some conditions under which a pairwise k-semistratifiable bitopological space is pariwise stratifiable. An open question posed in [18] is completely solved and results in [2] and [3] are extended to the setting of bitopological spaces. In the last section, we consider the quasi-pseudo-metrizability of a topological ordered spaces and provide a partial affirmative answer to an open problem of Künzi and Mushaandja in [15].…”