Infra soft topology is one of the recent generalizations of soft topology which is closed under finite intersection. Herein, we contribute to this structure by presenting two kinds of soft covering properties, namely, infra soft compact and infra soft Lindelöf spaces. We describe them using a family of infra soft closed sets and display their main properties. With the assistance of examples, we mention some classical topological properties that are invalid in the frame of infra soft topology and determine under which condition they are valid. We focus on studying the “transmission” of these concepts between infra soft topology and classical infra topology which helps us to discover the behaviours of these concepts in infra soft topology using their counterparts in classical infra topology and vice versa. Among the obtained results, these concepts are closed under infra soft homeomorphisms and finite product of soft spaces. Finally, we introduce the concept of fixed soft points and reveal main characterizations, especially those induced from infra soft compact spaces.

中文翻译：

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红外软紧致空间及其在不动点定理中的应用

基础软拓扑是最近在有限交点下闭合的软拓扑的推广之一。在这里，我们通过呈现两种软覆盖特性来为这种结构做出贡献，即红外线软致密空间和红外线软林德洛夫空间。我们使用一系列红外软闭集来描述它们并展示它们的主要特性。在例子的帮助下，我们提到了一些在软拓扑框架中无效的经典拓扑性质，并确定它们在什么条件下有效。我们专注于研究这些概念在软拓扑和经典基础拓扑之间的“传输”，这有助于我们使用经典基础拓扑中的对应物来发现这些概念在软拓扑中的行为，反之亦然。在得到的结果中，这些概念在基础软同胚和软空间的有限乘积下是封闭的。最后，我们介绍了固定软点的概念并揭示了主要特征，特别是那些由红外软紧凑空间引起的特征。