论文标题
关于Bornology的紧绷和拓扑游戏的某些观察
Certain observations on tightness and topological games in bornology
论文作者
论文摘要
本文是我们在功能空间中的调查$ c（x）$的延续，相对于$τ^s_ \ mathfrak {b} $在$ \ mathfrak {b} $上的强均匀融合{b} $（Chandra等人2020 \ cite et cite et cite {dcpdsd} and das and das et a al al al al a al a al a al。强大的统一融合（Beer and Levi，2009 \ Cite {bl}）在天生学上。首先，我们专注于$（c（x），τ^s_ \ mathfrak {b}）$的紧密属性概念及其某些变体，例如超近视，id-fan tightness和$ t $ - t $ - tughness。当$ c（x）$是{\ rm k}空间相对于拓扑$τ^s_ \ mathfrak {b} $时，讨论某些情况。接下来，引入了强$ \ mathfrak {b} $ - 打开游戏和$γ_ {\ mathfrak {b}^s} $ - 在$ x $上打开游戏，并研究了其一些后果。最后，我们考虑离散选择性属性和相关游戏。在$（c（x），τ^s_ \ mathfrak {b}）$上介绍了与离散选择性属性，$（c（x），τ^s_ \ mathfrak {b}）$的Gruenhage Game相关的拓扑游戏之间的几个交互。
This article is a continuation of our investigations in the function space $C(X)$ with respect to the topology $τ^s_\mathfrak{B}$ of strong uniform convergence on $\mathfrak{B}$ in line of (Chandra et al. 2020 \cite{dcpdsd} and Das et al. 2022 \cite{pddcsd-3}) using the idea of strong uniform convergence (Beer and Levi, 2009 \cite{bl}) on a bornology. First we focus on the notion of tightness property of $(C(X),τ^s_\mathfrak{B})$ and some of its variations such as supertightness, Id-fan tightness and $T$-tightness. Certain situations are discussed when $C(X)$ is a {\rm k}-space with respect to the topology $τ^s_\mathfrak{B}$. Next the notions of strong $\mathfrak{B}$-open game and $γ_{\mathfrak{B}^s}$-open game on $X$ are introduced and some of its consequences are investigated. Finally, we consider discretely selective property and related games. On $(C(X),τ^s_\mathfrak{B})$ several interactions between topological games related to discretely selective property, the Gruenhage game on $(C(X),τ^s_\mathfrak{B})$ and certain games on $X$ are presented.
