论文标题
一个无点的双架的组装及其两个变化
The assembly of a pointfree bispace and its two variations
论文作者
论文摘要
探索了粉饰双叶型作为无点的比特比特空间的双重性。特别是，研究了其所有点的Bisubspaces（即其生物Quotients）的订购集合。结果表明，该集合以三种有意义的方式是比特论的。特别是表明，除了汇编$ \ mathsf {a}（\ Mathcal {l}）$的firinital Biframe $ \ Mathcal {l} $之外，还有其他两个其他结构$ \ Mathsf {a} _} _ {cf}（cf}（cf}（cf}（cf}（\ mathcal {\ mathcal {l}）$ {\ mathcal {\ n} $ {\ mathcal {\ mathcal {\ mathcal {l}）$ $ \ mathsf {a} _ {\ pm}（\ Mathcal {l}）$，它们的主组件与$ \ Mathsf {a}（\ Mathcal {l}）$具有相同的主组件。 $ \ Mathsf {a} _ {cf}（\ Mathcal {l}）$和$ \ Mathsf {a} _ {\ pm}（\ Mathcal {l}）$的主要组成部分是$ \ Mathcal的所有Biquotients。结构$ \ mathsf {a} _ {cf}（\ mathcal {l}）$是双frame，表明所有生物质量的集合是由粘合的生物Quotients的框架以及贴片拟合的框架生成的。结构$ \ mathsf {a} _ {\ pm}（\ mathcal {l}）$作为双形式显示所有生物品质的集合是由正面生物品质的框架以及负面生物的框架生成的。引入了限制双帧的适应性和亚拟合的概念，并显示出了在Picado和Pultr（2011）中出现的这些公理的两个表征定理的类似物。这些定理的空间，比特版本已被证明，其中频谱为$ t_1 $的finarity Biframes是特征的，除其他方面，$ \ mathsf {a} _} _ {cf}（\ mathcal {l}）$。
The duality of finitary biframes as pointfree bitopological spaces is explored. In particular, for a finitary biframe $\mathcal{L}$ the ordered collection of all its pointfree bisubspaces (i.e. its biquotients) is studied. It is shown that this collection is bitopological in three meaningful ways. In particular it is shown that, apart from the assembly $\mathsf{A}(\mathcal{L})$ of a finitary biframe $\mathcal{L}$, there are two other structures $\mathsf{A}_{cf}(\mathcal{L})$ and $\mathsf{A}_{\pm}(\mathcal{L})$, which both have the same main component as $\mathsf{A}(\mathcal{L})$. The main component of both $\mathsf{A}_{cf}(\mathcal{L})$ and $\mathsf{A}_{\pm}(\mathcal{L})$ is the ordered collection of all biquotients of $\mathcal{L}$. The structure $\mathsf{A}_{cf}(\mathcal{L})$ being a biframe shows that the collection of all biquotients is generated by the frame of the patch-closed biquotients together with that of the patch-fitted ones. The structure $\mathsf{A}_{\pm}(\mathcal{L})$ being a biframe shows the collection of all biquotients is generated by the frame of the positive biquotients together with that of the negative ones. Notions of fitness and subfitness for finitary biframes are introduced, and it is shown that the analogues of both characterization theorems for these axioms appearing in Picado and Pultr (2011) hold. A spatial, bitopological version of these theorems is proven, in which finitary biframes whose spectrum is pairwise $T_1$ are characterized, among other things in terms of the spectrum of $\mathsf{A}_{cf}(\mathcal{L})$.
