Back in the fall I did some work on getting hacklab.to‘s 3d-printer to print mathematical objects created in sage. Unfortunately, shortly after I got it to work and printed a test sphere, the 3d printer broke. Thus began a long succession of the makerbot — nicknamed the break-r-bot — being fixed and broken… spending most of its time broken.
But recently it was fixed and I decided to dig out my old code and get to work on it.
A couple days a go, I saw some nice visualisations of separation axioms on Wikipedia. Unfortunately, it wasn’t a full set. Well, here is a full set (well, T0, T1, T2, T2 1/2, T3, T4, T5):
Here’s the first revision of a graph of the implications of topological properties that I made:
(Click on it to see a better version!)
It’s mostly based off the stuff in Counterexamples In Topology (great book, BTW) but I did add some stuff (like Baire!) and merged/reorganised it. Diagram was made by Graphviz.
Most of the implications are trivial, but there are a few I haven’t prooved yet (most of the ones involving seperation axioms).
