设E是一个A rch im edean R iesz空间,a∈E,Φ≠A E,则有如下的两个结论:1)由a生成的a-拓扑空间E是一个H ausdorff空间;2)若以下条件之一成立,则由A生成的A-拓扑空间E是一个H ausdorff空间:(a)子集{a:a∈A}有上界;(b)E具有强单位元;(c)若E=C(X),其中X是一个局部紧H ausdorff空间.
本文依托超星学习通平台探讨了工科数学分析N课程学生个性化学习的方法和途径,并进行了初步应用。针对当前课程教与学的现状,本文通过建设课程知识图谱,提出了应用知识图谱和AI助教实现学生个性化学习的途径。应用表明知识图谱的关联知识点、学习资料可促进学生的自主个性学习;知识图谱运用统计的学习数据,为学生自主规划学习路径提供可能性,同时为教师提供精确的学生知识的掌握情况,便于教师进一步对学生进行个性化指导。此外,AI助教可为学生高效地提供答疑解惑和个性化学习问答。知识图谱和AI助教为学生的个性化学习提供了现实途径,也为进一步提升教学质量带来了极大可能性。Based on the platform of Chaoxing learning, this paper discusses the methods and approaches of personalized learning for students of the N course of Engineering Mathematical Analysis, and makes a preliminary application. According to the current situation of curriculum teaching and learning, this paper proposes a way to realize students’ personalized learning by using knowledge graph and AI teaching assistant through the construction of curriculum knowledge graph. The application shows that the related knowledge points and learning materials of knowledge graph can promote the students’ independent learning. Knowledge graph can use statistical learning data to plan personalized learning paths for students, and provide teachers with accurate knowledge of students, which is convenient for teachers to further personalized guidance for students. In addition, AI teaching assistants can provide students with efficient question-and-answer and personalized learning questions. Knowledge graph and AI teaching assistant provide a practical way for students to personalized learning, and also bring great possibilities for further improving the quality of teaching.
