中文摘要：

在拓扑空间中引入理想结构就形成了理想拓扑空间,理想拓扑空间体现了拓扑结构和理想结构的融合,是一类重要的拓扑空间,研究它具有重要的理论价值.给出了I-正则空间和I-正规空间的映射定理及拓扑和定理,得到了I-正规空间的一些特征.并讨论了I-正则空间、I-正规空间和I-紧空间之间的关系.

英文摘要：

Introducing ideal structures in topological spaces forms an ideal topological space. An ideal topolo-gical space reflects the integration of topological structures and ideal structures, and then is a kind of important to-pological space. Researching on it has important theoretical value. Map theorem and topological sum theorem on I-regular （ resp. I-normal） spaces are given respectively. Some characterizations of I-normal spaces are obtained. Moreover, the relationship among I-regular, I-normal and I-compact spaces are discussed.