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A beautifully told story with colorful characters out of epic tradition, a tight and complex plot, and solid pacing. -- Booklist, starred review of On the Razor's Edge

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Monday, October 10, 2016

Mathematica Antiqua

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This is a reposting of something that was on the Auld Blogge at LiveJournal. I cannot now use LiveJournal since some sort of virus has squatted on the page and insists on popping up new tabs that promise to remove the very obstacle in questions. However, I was able to use navigation keys to capture and paste the material here for posterity

A Blast from the Past

Last week (sic) I received a comment on this blog from my old topology professor, Doug Harris. This has sent my brain on a stroll down memory lane. I wrote a master's thesis under him that resulted in an original theorem or two. I have always taken great pride in the fact that they were of no practical use whatsoever. It appears now that the field of function space topologies has now become a hot new topic, and so the danger has arisen that someone somewhere may actually cite "Flynn's Theorem."

Now I remember a much younger professor, with darker hair. Of course, I also remember a much younger graduate student several pounds lighter. When I was there, he was the topology guy. Later, he moved into computer science, internet, and stuff like that; although he still has an interest in topology and is working on an interesting spectral theory of commutative rings with unit. He writes at spectral.mscs.mu.edu/GeneralTopology/ that

"My later work discovered some specific simple topological spaces which could act as "prime numbers" for constructing and characterizing very general classes of spaces. That is, any space in the class can be constructed from my spaces, which is the easy part, but if my spaces are constructed from other spaces one of the other spaces must be one of mine: that is the hard part, the primeness, and is something very unusual in topology."

One of the theorems in my own master thesis was that any function space topology in a class could be described as a subspace of a product of a particular space of the class, which I called the universal space of that class. So there is a distant analogy here that tickles me. The theorem was later published in a math journal, and so is my first publication, albeit not SF. Okay, so I had some stories published in my high school literary magazine; but they don't count because I was one of the two editors. But I digress. By some weird coincidence I had come across a copy of the paper and had been thinking about the Old Days. I had even pulled down Schubert, Dugundji and some other texts and was doing a little recreational reading. And then along comes the comment from Prof. Harris. How weird is that?

(Not that weird. I pulled those books out of storage when Margie built me an office with lots of bookcases, and from time to time I ave looked in one or another of the books. Tensor Analysis on Manifolds. Rings of Continuous Functions. Fundamentals of Linear Algebra. Woo hoo. So I have looked in the Topology books before without calling up spirits from the vasty deep.)

Some of you may be wondering, What the @#$%^ is topology, and thinking it has something to do with maps. It does; but not those kinds of maps. Perhaps I will post on the subject and elevate the tone of this blog. But for a sum of money I will not. You have been warned.

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