中文摘要：

本文研究粗糙集与拓扑空间的关系，统一地使用拓扑空间中的集合关于子基的内部和闭包来研究粗糙集理论和覆盖广义粗糙集理论中的下近似集和上近似集，以及由它们导出的关于子基的开集，导集，闭集，边界，研究这两个概念及由它们导出的相关概念的性质不仅对于粗糙集理论，而且对于拓扑学本身都有重要的理论和实际应用意义。

英文摘要：

We study the relationships between the rough sets and the topological space, define the interior operator and the closure operator generated by a subbase of a topological space. which are conjugated with a lower approxfination and an upper approximation, and obtain their basic properties. These results can be considered as fundamental theory of rough sets.