标题： 与拓扑空间中可生成结构相关的选择原理的一些结果 显示英文标题

标题： Certain results on selection principles associated with bornological structure in topological spaces

摘要： We study selection principles related to bornological covers in a topological space $X$ following the work of Aurichi et al., 2019, where selection principles have been investigated in the function space $C_\mathfrak{B}(X)$ endowed with the topology $\tau_\mathfrak{B}$ of uniform convergence on bornology $\mathfrak{B}$. We show equivalences among certain selection principles and present some game theoretic observations involving bornological covers. We investigate selection principles on the product space $X^n$ equipped with the product bornolgy $\mathfrak{B}^n$, $n\in \omega$. 考虑到如无界数（$\mathfrak{b}$）、支配数（$\mathfrak{d}$）、伪交集数（$\mathfrak{p}$）等基数不变量，我们建立了具有某些选择原则的出生范畴基的基数之间的联系。最后，我们研究了$C_\mathfrak{B}(X)$的紧性性质的一些变化，并以$X$的选择性出生范畴覆盖性质来描述它们。 显示英文摘要

摘要： We study selection principles related to bornological covers in a topological space $X$ following the work of Aurichi et al., 2019, where selection principles have been investigated in the function space $C_\mathfrak{B}(X)$ endowed with the topology $\tau_\mathfrak{B}$ of uniform convergence on bornology $\mathfrak{B}$. We show equivalences among certain selection principles and present some game theoretic observations involving bornological covers. We investigate selection principles on the product space $X^n$ equipped with the product bornolgy $\mathfrak{B}^n$, $n\in \omega$. Considering the cardinal invariants such as the unbounding number ($\mathfrak{b}$), dominating numbers ($\mathfrak{d}$), pseudointersection numbers ($\mathfrak{p}$) etc., we establish connections between the cardinality of base of a bornology with certain selection principles. Finally, we investigate some variations of the tightness properties of $C_\mathfrak{B}(X)$ and present their characterizations in terms of selective bornological covering properties of $X$.