subtle and profound meaning in English

精微深远

So far , mathematicians who study topology have obtained substantial achievements in important topological directions , such as generalized metric space , cardinal function , compactness , dimension theory , etc . but what is worth to paying attention to is that we often draw on one special type of topological space to think and solve problems , for example , the classical structures , sorgenfrey line k , michael line rq , niemytzki planetv , kxk , # q xp , etc . ; subtle and profound topological properties aredetailedly characterized by them
而值得注意的是，在一般拓扑学的研究历史中，我们常常借助一类特殊的空间来思考和解决问题，如我们熟悉的经典构造： sorgenfrey直线k 、 michael直线r _ q 、 niemytzki平面n 、 k k 、 r _ q p等等，漂亮地刻画了细微而深奥的拓扑性质。