论文标题
加权弱的广义准则空间和半层次
Weakly weighted generalised quasi-metric spaces and semilattices
论文作者
论文摘要
通过在动态系统中熵理论的最新应用中，我们概括了Matthews引入的概念，并定义了弱加权和组成的弱加权（广义）准量表。然后，我们将这些对象与理论计算机科学和动力学中产生的其他结构之间的对应关系进行系统化并扩展到一般性。特别是，我们研究了弱部分指标的对应关系，如果基础空间是半静脉，则具有不变（广义）准米分析，以满足降值路径条件，并且具有严格的单调半（-co-）估值。我们总结说，讨论了通用准中性半层次的内态性，即对已知的内在半熵熵和半群熵的概括。
Motivated by recent applications to entropy theory in dynamical systems, we generalise notions introduced by Matthews and define weakly weighted and componentwisely weakly weighted (generalised) quasi-metrics. We then systematise and extend to full generality the correspondences between these objects and other structures arising in theoretical computer science and dynamics. In particular, we study the correspondences with weak partial metrics, and, if the underlying space is a semilattice, with invariant (generalised) quasi-metrics satisfying the descending path condition, and with strictly monotone semi(-co-)valuations. We conclude discussing, for endomorphisms of generalised quasi-metric semilattices, a generalisation of both the known intrinsic semilattice entropy and the semigroup entropy.
