We study the possibility to get a sequential characterization of the compactness of a set with respect to a cone. Then, we consider some set-equilibrium problems (whose formulations are inspired by set-optimization problems) and in the study of the existence of a solution of these problems we employ the generalized compactness investigated before. Several technical tools are needed throughout the presentation in order to fulfill these objectives. Furthermore, several illustrating examples are presented in order to clearly motivate our theoretical results.

中文翻译：

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集合的锥紧性及其在集合平衡问题中的应用

我们研究了获得集合相对于圆锥的紧性的顺序特征的可能性。然后，我们考虑一些集合平衡问题（其公式受到集合优化问题的启发），并且在研究这些问题的解的存在性时，我们采用之前研究的广义紧性。为了实现这些目标，整个演示过程中需要多种技术工具。此外，还提供了几个说明性示例，以便清楚地激发我们的理论结果。