本文在第一章中简单的介绍了拓扑空间理论的形成，以及与覆盖性质、超空间相关的一些的知识。
In the first chapter, the formation of topological space theory is simply introduced, as well as some knowledge about covering property and hyperspaces.
本文的主要目的是在不具任何凸结构的一般拓扑空间中研究KKM理论及其应用。
This paper is aimed to study the KKM theory and its applications in general topological Spaces without any convexity structure.
利用超距空间的基本性质及拓扑空间紧致性的相关理论，给出超距空间为紧致空间的充分且必要条件，并讨论了一些相关性质。
A sufficient and necessary condition in terms of the compactness of super-distance space is given based on the property of super-distance space and the related theory of compactness.
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