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This article is a continuation of our investigations in the function space$C(X)$ with respect to the topology $\tau^s_\mathfrak{B}$ of strong uniformconvergence on $\mathfrak{B}$ in line of (Chandra et al. 2020 \cite{dcpdsd} andDas 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 oftightness property of $(C(X),\tau^s_\mathfrak{B})$ and some of its variationssuch as supertightness, Id-fan tightness and $T$-tightness. Certain situationsare discussed when $C(X)$ is a {\rm k}-space with respect to the topology$\tau^s_\mathfrak{B}$. Next the notions of strong $\mathfrak{B}$-open game and$\gamma_{\mathfrak{B}^s}$-open game on $X$ are introduced and some of itsconsequences are investigated. Finally, we consider discretely selectiveproperty and related games. On $(C(X),\tau^s_\mathfrak{B})$ severalinteractions between topological games related to discretely selectiveproperty, the Gruenhage game on $(C(X),\tau^s_\mathfrak{B})$ and certain gameson $X$ are presented.

Certain observations on tightness and topological games in bornology