本文是在（Chandra et al. 2020）中利用度量空间上的强一致收敛性（Beer and Levi，2009）的思想对度量空间中的度量开覆盖和相关选择原理进行研究的延续。在这里，我们探索进一步的分支，提出各种选择原则的特征，涉及到某些类的代数覆盖使用的Ramseyan划分关系，互动的结果之间的基数的代数基础和某些选择原则，涉及代数覆盖，产生了新的观测资料的$\mathfrak{B}^s$ -Hurewicz属性介绍，（Chandra et al. 2020）以及$X$的$\mathfrak{B}^s$ -Gerlits-Nagy性质的几个结果（Gerlits和Nagy，1982）。此外，在有限幂$X^n$与乘积拓扑$\mathfrak{B}^n$中，$X^n$的${\mathfrak{B}^n}^s$-Hurewicz性质以及$X^n$的${\mathfrak{B}^n}^s$-Gerlits-Nagy性质用$(C(X),τ^s_\mathfrak{B})$的可数扇紧性、可数强扇紧性以及Reznichenko性质来刻画.
英文摘要：
This article is a continuation of the study of bornological open covers and related selection principles in metric spaces done in (Chandra et al. 2020) using the idea of strong uniform convergence (Beer and Levi, 2009) on bornology. Here we explore further ramifications, presenting characterizations of various selection principles related to certain classes of bornological covers using the Ramseyan partition relations, interactive results between the cardinalities of bornological bases and certain selection principles involving bornological covers, producing new observations on the $\mathfrak{B}^s$-Hurewicz property introduced in (Chandra et al. 2020) and several results on the $\mathfrak{B}^s$-Gerlits-Nagy property of $X$ which is introduced here following the seminal work of (Gerlits and Nagy, 1982). In addition, in the finite power $X^n$ with the product bornology $\mathfrak{B}^n$, the ${\mathfrak{B}^n}^s$-Hurewicz property as well as the ${\mathfrak{B}^n}^s$-Gerlits-Nagy property of $X^n$ are characterized in terms of properties of $(C(X),τ^s_\mathfrak{B})$ like countable fan tightness, countable strong fan tightness along with the Reznichenko's property.
我们提出了一个新的变化的经典选择原则$\mathsf{S}_\mathrm{k}(\mathcal A, \mathcal B)$（$k\in\mathbb N$）和$\mathsf{S}_\mathrm{fin}(\mathcal A, \mathcal B)$，正式位于这两个属性之间。在经典的选择原则的情况下，我们也得到了一个新的变化的拓扑游戏，并讨论如何新的拓扑性质可能会出现在特定的情况下，覆盖和紧。
Projective versions of the properties in the Scheepers Diagram
设$\mathcal{P}$为拓扑性质。A. V. Arhangel'skii称$X$投影为$\mathcal{P}$，如果$X$的每第二个可数连续像是$\mathcal{P}$。LJ.D.R. Ko $\check{c}$在$\mathbb{R}^ω$中用连续象刻画了Menger，Rothberger，Hurewicz和Gerlits-Nagy的经典覆盖性质.本文研究了Scheepers图中选择性质的所有投影形式的函数刻画。
