π-base

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”.

Important: π-base is updating constantly and my website is not updating as fast, so some theorems may be in an outdated form.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).

By ID: 0xx, 1xx, 2xx, 3xx, 4xx, 5xx, 6xx, 7xx.

By difficulty: 1, 2.