Contents: Introduction. - Fundamental Concepts. - Topological Vector Spaces.- The Quotient Topology. - Completion of Metric Spaces. - Homotopy. - The Two Countability Axioms. - CW-Complexes. - Construction of Continuous Functions on Topological Spaces. - Covering Spaces. - The Theorem of Tychonoff. - Set Theory (by T. Br|cker). - References. - Table of Symbols. -Index.
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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)
还没人写过短评呢
还没人写过短评呢