set theoretic topology Dec 30, 2010

Set theoretic topology is the application of set theory to the field of topology. Topology is about holes; STT is about sets of holes. A question a set theoretic topologist would ask might be: What does the set of all sets of holes look like? It turns out it looks just like the integers. The practical applications of this are obvious: if you add two donuts together, you get a two-holed donut (shaped like an eight). If you multiply two donuts (imagine convolving the surfaces of the donuts through the fourth dimension), you will be left with only one regular donut. Don't. Multiply. Donuts. It is a waste of perfectly good holes. I hear you asking, what if I create a field of N-donuts (you will need negative donuts for this) and I want it to be algebraically closed? Well, get ready for imaginary holes. I had a dream once in which I was describing a wall outside of a city as "like a hole. Well, actually, an unhole. Where there's stuff--- that shouldn't be there." That's what imaginary holes are like, except they can rotate into reality and when they do, the stuff that used to be real is now imaginary. Don't do this if you plan to eat the donuts later! Anyway, the field closes right after you get the imaginary donuts to stick there, and you can't get back in without the key which is in the maze by the skeleton. Anyway, thank you for taking the time to read my writeup on set theoretic topology.