General Topology
by John Leroy Kelley, Sam Sloan · first published 2008
13mentions
2recommended by
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2013–2024first – last mentioned
67% recommend33% neutral
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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
on “Ask HN: What books do you keep on your desk?” ↗…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????
on “This Message Does Not Exist” ↗…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…
on “Probability Theory for Scientists and Engineers” ↗…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…
on “The Brilliance of a Stradivari Violin Might Rest Within Its Wood” ↗…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…
on “Designing a Business Card in LaTeX” ↗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.…
on “The Two Cultures of Mathematics (2000) [pdf]” ↗On orals, I did some!! Maybe the first was as a senior. I got Kelley, General Topology and once a week gave a lecture to a prof! One week a chapter, and the next some exercises! It was fun! The next time was on a written qualifying exam: The exam had an error, and I wasted time trying…
on “School is all about signaling, not skill-building” ↗…a favorite book. Halmos was the best writer of the bunch. And I read through Spivak. Most difficult undergraduate course in the country? Not really! As a senior I took a reading course from Kelley, General Topology where I gave the lectures -- usually Kelley was more difficult than any of Halmos. ..., Spivak! Just what could be so difficult about a freshman physics course, I don't know! The Feynman lectures are…
on “Steve Ballmer's Harvard CS50 Lecture Yesterday” ↗…all the t's -- and less good than desired instead of better. The other two courses they had me in were close to what I'd already studied carefully in ugrad school. One of these two was from Kelley, General Topology that I had lectured from to a prof. I did well at my ugrad teaching, started violin, met my wife, and got a Ph.D. in applied math later at another university. There, too, at times I did work comparable…
on “Physicists link two time crystals in seemingly impossible experiment” ↗…average SAT scores over 700, but did get accepted in the math (or statistics) department as a graduate student. I'd read lots of John Tukey's work -- uniformity in topology (in the back of Kelley's 'General Topology'), Tukey's lemma in axiomatic set theory, stepwise regression, power spectral estimation (Blackman and Tukey), the FFT (Cooley and Tukey), and 'Exploratory Data Analysis', had been working in applied…
on “I cannot afford to go back to engineering school” ↗> 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.…
on “The Two Cultures of Mathematics (2000) [pdf]” ↗Another view of topology is in John L.\ Kelley, {\it General Topology,\/} D.\ Van Nostrand, Princeton, 1955.\ \ In the set R of the real numbers and x, y in R with x < y, (x,y) = { z | x < z < y } is open and, with x <= y, [x,y] = { z | x <= z <= y } is closed. A…
on “This open problem taught me what topology is [video]” ↗…After several hundred e-mail messages sent, I never pitched a VC. But I've done lots of successful pitches elsewhere, academics, technical work, in business. As an undergrad math major, I got Kelley, 'General Topology', read it, and gave lectures to a prof -- so, I had practice lecturing. I've done lots of college and grad school teaching. E.g., in a software house, I corrected some engineers of our customer, found…
on “Marc Andreessen at Startup School [video]” ↗