I think the worst terminology in all of mathematics may be that of G-delta and F-sigma sets. Even though I learned the meaning of them years ago, they still convey no information to me at first glance. I just looked at the definitions of perfectly normal space and Baire set, and without concentrating on that mysterious G-delta they mean nothing to me. Good terminology should provide a hint as why the definition isn’t some other way. Why not F-sigma sets? G-delta-sigma sets? G-sigma-delta sets?

Which is too bad, because in both instances the property is completely natural. The perfectly normal spaces are exactly those spaces where every closed set is a zero set of a continuous function. The Baire sets are for doing measure theory when you’re outside the friendly confines of a perfectly normal space. To integrate real-valued bounded continuous functions, we only need to consider Baire sets. Other sets are uninteresting from the point of view of measure theory. But in both cases it’s easier to work back from the desired property to the definition than vice versa.

Mark Chu-Carroll draws attention to a Baptist high school that has managed to work God into the curriculum of its math classes.

One commenter, CRM-114, asks

BTW, what if they get a Jew or Muslim in the geometry class? Do they get alternative instruction fitting their religion?

which leads to another commenter, chaos_engineer, writing the greatest comment in the history of the internet.

Of course. Christians would be taught real geometry, with the Euclidean version of the parallel postulate.

People who practice flawed religions would naturally be more comfortable studying flawed, non-Euclidean geometries. Jews could learn Riemann’s version of the parallel postulate, Muslims could learn Lobachevksy’s, and atheists could learn H. P. Lovecraft’s.

Peter Woit reports that the entire editorial board of the journal K-Theory (published by Springer) has resigned. The current editors have already formed a new journal, Journal of K-Theory, which will be distributed by Cambridge University Press.

The subscription price for the Springer journal was $1590. The subscription price for the new journal is 380 British pounds, which is roughly half the price.

Alexandre Borovik writes about a disturbing story coming out of Turkey. Ali Nesin organizes a summer school in mathematics in a village near Epheseus in Turkey. For some sort of bureaucratic rule violations (including “education without permission”), he has been arrested and the school has been shut down.

Alexandre has a follow-up post with more details, and a online petition. Contact details are provided if you want to add your name to the petition.

I was thinking about nets the other day, when I was reminded of something that I wondered when I first encountered them. Is the generalization to partially-ordered sets strictly necessary? The generalization to partially-ordered sets is useful, but are there spaces with points that are not reachable by totally-ordered nets alone?

In a first countable space, a point lies in the closure of a set if and only if there is a sequence of points in the set that converges to the point. This property fails in general. For example, an uncountable set with the cofinite topology has no non-trivial convergent sequences, but the closure of any infinite set is the whole space. You can recover this property if you pass to nets, which allow fairly general partially-ordered sets to be the index set (the only requirement you must impose is that they be directed sets). So if you require the index sets of your nets to be totally ordered, is there a space which contains a point that is not the limit of such a net?

Poking around Wikipedia, I found that the page for order topology, which suggests that the Tychonoff plank is an example of a space where totally-ordered nets are not sufficient. The page discusses nets indexed by ordinals, which possibly is a loophole, but it seems like a very narrow one. I’d be curious if anyone knows for sure.