This little section of my blog is dedicated to my own proofs of as many theorems in π-base as possible. Could be used as a reference to all the proofs in one single place, instead of relying on looking through the books their website is referencing (keep in mind, the simpler proofs are mine — a.k.a likely less elegant than from other sources — and the harder proofs taken from other sources were adapted to fit my writing style.
They don’t have many pre-requisites to understand them (except for, of course, knowing the concepts of topology). Every instance of “neighborhood” is shortened to “nbd”, and there is no harm in assuming a nbd is open whenever needed. I make sure to point out any usage of the axiom of choice in the proofs, but the axiom of countable choice is so essential to so many topological arguments that it is always used without mention.
Important: π-base is updating constantly and my website is not updating as fast, so some theorems may be in an outdated form. The last update was: Mar 11, 2026.
You can list through my proofs by ID or by difficulty (a personal metric, of course). Alternatively, you can see the latest 50 proofs.