Once, whenI was still a student at Tübingen, I was grading some exercises after a lecture on these fundamental concepts. In the lecture it had already been established that a set is open if and only if all of its points are interior, and one exercise went like this: Show that the set of interior points of a set is always open. In came a student asking why we had not accepted his reasoning: "The set of interior points contains only interior points(an indisputable tautology); hence, the problem is trivial." There were a couple of other graders present and we all zealously tried to convince him that in talking about interior points you have to specify what set they are interior to, but in vain. When he realized what we wantd, he left, calmly remarking that we were splitting hairs. What could ... (查看原文)
2 有用 邻家大爷 2012-05-29 19:52:07
浏览了一遍，很有意思的科普书
2 有用 7086 2024-11-23 20:57:16 陕西
挺有意思的书，简练而不失严谨与丰富。穿插着略去了证明的有趣事实，可以当做习题来练自己。其实拓扑学是个框架，点集X是用户自定义的，集族O由X的哪些子集组成也是用户自定义的。只要O里的元素满足三条开集公理，O就有资格作为一个拓扑，而其元素也就荣获“开集”称号，并享有拓扑空间会员特权，例如可以定义连续映射、收敛序列。进一步充值豪斯多夫超级会员，还可享受序列收敛于唯一点等权益哟😘
2 有用 才难破赋意 2019-05-21 22:43:30
将拓扑学讲的妙趣横生
4 有用 Grasie 2015-04-18 18:35:47
迄今看过最搞笑的数学书（褒义）
2 有用 行者 2021-12-16 19:22:30
碎碎念很多，但好多精华也在里面，有些怀疑初学者是否能够完全领悟。图很多，强调直观，这一点对初学者很友好。总的来说，适合想感受一下拓扑为何物的初学者，但有些精华处大概需要有些历练之后再看看大概会有新的感受。