成对$k$ -半层双空间与拓扑序空间
Pairwise $k$-Semi-Stratifiable Bispaces and Topological Ordered Spaces
摘要：
本文继续研究两两（$k$ -半）可层双拓扑空间。给出了成对$k$ -半层双拓扑空间的一些新的刻画。进一步研究了两两可层和两两$k$ -半层双拓扑空间之间的关系，解决了Li和Lin最近在\cite{LL}中提出的一个公开问题.我们还研究了拓扑序空间$(X, τ, \preccurlyeq)$的拟伪度量性。证明了若$(X, τ, \preccurlyeq)$是球传递拓扑序$C$ -和$I$ -空间，使得$τ$是可度量化的，则它的双拓扑空间$(X,τ^{\flat},τ^{\natural})$是拟伪可度量化的.该结果为\cite{KM}中的一个问题提供了部分肯定的答案。
英文摘要：
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 \cite{LL} is completely solved. We also study the quasi-pseudo-metrizability of a topological ordered space $(X, τ, \preccurlyeq)$. It is shown that if $(X, τ, \preccurlyeq)$ is a ball transitive topological ordered $C$- and $I$-space such that $τ$ is metrizable, then its associated bitopological space $(X,τ^{\flat},τ^{\natural})$ is quasi-pseudo-metrizable. This result provides a partial affirmative answer to a problem in \cite{KM}.
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