无论在家还是办公室，手边永远常备这几本：Rudin 的《Real and Complex Analysis》、Halmos 的《Finite Dimensional Vector Spaces》、Billingsley 的《Probability and Measure》、Kelley 的《General Topology》、Lang 的《Undergraduate Algebra》、Simmons 的《Introduction to Topology and Modern Analysis》、Parthasarathy 的《Probability Measures on Metric Spaces》、Whinston, Green 和 Mas-Colell 的《Microeconomic Theory》
Always within arm's reach at both home and work: Rudin, Real and Complex Analysis Halmos, Finite Dimensional Vector Spaces Billingsley, Probability and Measure Kelley, General Topology Lang, Undergraduate Algebra Simmons, Introduction to Topology and Modern Analysis Parthasarathy, Probability Measures on Metric Spaces Whinston, Green and Mas-Colell, Microeconomic Theory
……只由元素组成。这是个不错的修正。想了解更多的话，有优雅且流行已久的 P. Halmos 的《Naive Set Theory》，现在有 PDF、LaTeX 等版本。还有 J. Kelley 的《General Topology》附录。还有 P. Suppes 的《Axiomatic Set Theory》。想再看更多？你确定还想看？？？？
…consist only of elements. That's a good fix. For more, there is the elegant, long popular, P. Halmos Naive Set Theory, now available in PDF, LaTeX, etc. For more there is the appendix to J. Kelley, General Topology. For more there is P. Suppes, Axiomatic Set Theory. For more, sure you want more????
…we can use topologies to define continuous functions where epsilon and delta and where converging sequences don't work. If curious, look up Moore-Smith convergence, nets, and filters or just Kelley, General Topology. Well, a sigma algebra is like a topology, that is, is a collection of subsets: A sigma algebra is closed under countable unions and relative complements. Right, we avoid uncountable unions because…
…put me in courses beneath me and courses irrelevant to the math I wanted. For "beneath", they put me in a course in point-set topology. Maybe okay: First lecture I learned that the text was Kelley, General Topology. Heck, as an undergraduate I'd already gotten a copy and a reading course, read the thing, and gave lectures once a week to a prof. One week I explained a chapter and the next week worked exercises…
…its usual meaning without defining it, and then he saw that my solution was better than his and I was off the carpet. Bummer. He was too quick to cut me off at the knees. (2) Course was in Kelley, General Topology. As a ugrad senior, I'd lectured a prof once a week and covered all of it except the last chapter on compactness when I cut out to finish my honors paper [The typing was so hard that from rolling the…
Kelley 那本纯数书《General Topology》致谢了 1950-1952 年间美国国家科学基金会（NSF）和海军研究办公室的资助。同一批资助方还资助了 Luenberger 的《Optimization by Vector Space Methods》——在 Hahn-Banach 定理里找乐子。……
The Kelley, General Topology pure math book acknowledges NSF and Office of Naval Research support in years 1950-1952. Same financial supporters for Luenberger, Optimization by Vector Space Methods -- fun with the Hahn-Banach theorem.…
无论在家还是办公室，手边永远常备这几本：Rudin 的《Real and Complex Analysis》、Halmos 的《Finite Dimensional Vector Spaces》、Billingsley 的《Probability and Measure》、Kelley 的《General Topology》、Lang 的《Undergraduate Algebra》、Simmons 的《Introduction to Topology and Modern Analysis》、Parthasarathy 的《Probability Measures on Metric Spaces》、Whinston, Green 和 Mas-Colell 的《Microeconomic Theory》
Always within arm's reach at both home and work: Rudin, Real and Complex Analysis Halmos, Finite Dimensional Vector Spaces Billingsley, Probability and Measure Kelley, General Topology Lang, Undergraduate Algebra Simmons, Introduction to Topology and Modern Analysis Parthasarathy, Probability Measures on Metric Spaces Whinston, Green and Mas-Colell, Microeconomic Theory
……只由元素组成。这是个不错的修正。想了解更多的话，有优雅且流行已久的 P. Halmos 的《Naive Set Theory》，现在有 PDF、LaTeX 等版本。还有 J. Kelley 的《General Topology》附录。还有 P. Suppes 的《Axiomatic Set Theory》。想再看更多？你确定还想看？？？？
…consist only of elements. That's a good fix. For more, there is the elegant, long popular, P. Halmos Naive Set Theory, now available in PDF, LaTeX, etc. For more there is the appendix to J. Kelley, General Topology. For more there is P. Suppes, Axiomatic Set Theory. For more, sure you want more????
……在 epsilon 和 delta 失效、收敛序列也不管用的时候，我们可以利用拓扑来定义连续函数。如果好奇的话，去查查 Moore-Smith 收敛、网（net）和滤子（filter），或者直接看 Kelley 的《General Topology》。嗯，sigma 代数就像一个拓扑，也就是说，它是一个子集族：sigma 代数在可数并集和相对补集下是封闭的。对，我们避开不可数并集是因为……
…we can use topologies to define continuous functions where epsilon and delta and where converging sequences don't work. If curious, look up Moore-Smith convergence, nets, and filters or just Kelley, General Topology. Well, a sigma algebra is like a topology, that is, is a collection of subsets: A sigma algebra is closed under countable unions and relative complements. Right, we avoid uncountable unions because…
……把我塞进了一些水平远低于我、而且跟我想要的数学毫不相关的课程里。说到“低于我”，他们把我塞进了一门点集拓扑课。本来或许还行：第一节课我发现教材居然是 Kelley 的《General Topology》。搞毛啊，我本科时早就弄了一本来精读，把整本书啃完了，还每周给一位教授讲一次课。一周讲一章，下一周做习题……
…put me in courses beneath me and courses irrelevant to the math I wanted. For "beneath", they put me in a course in point-set topology. Maybe okay: First lecture I learned that the text was Kelley, General Topology. Heck, as an undergraduate I'd already gotten a copy and a reading course, read the thing, and gave lectures once a week to a prof. One week I explained a chapter and the next week worked exercises…
……按通常的含义来用却没给定义，接着他发现我的解法比他的更好，我就被免除挨训了。真扫兴。他太急着把我压下去了。(2) 课程教材是 Kelley 的《General Topology》。我大四时每周给教授讲一次课，除了讲紧致性的最后一章因为我要抽身完成荣誉论文没讲之外，全书都讲完了［打字太费劲了，光是转动滚筒……
…its usual meaning without defining it, and then he saw that my solution was better than his and I was off the carpet. Bummer. He was too quick to cut me off at the knees. (2) Course was in Kelley, General Topology. As a ugrad senior, I'd lectured a prof once a week and covered all of it except the last chapter on compactness when I cut out to finish my honors paper [The typing was so hard that from rolling the…
Kelley 那本纯数书《General Topology》致谢了 1950-1952 年间美国国家科学基金会（NSF）和海军研究办公室的资助。同一批资助方还资助了 Luenberger 的《Optimization by Vector Space Methods》——在 Hahn-Banach 定理里找乐子。……
The Kelley, General Topology pure math book acknowledges NSF and Office of Naval Research support in years 1950-1952. Same financial supporters for Luenberger, Optimization by Vector Space Methods -- fun with the Hahn-Banach theorem.…