This blog post is a continuation of today's episode on PBS Infinite Series, "Topology vs. 'a' Topology." My hope is that this episode and post will be helpful to anyone who's heard of topology and thought, "Hey! This sounds cool!" then picked up a book (or asked Google) to learn more, only to find those formidable three axioms of 'a topology' that, admittedly do not sound cool. But it turns out those axioms are what's "under the hood" of the whole topological business! So without further ado, let's pick up where we left off in the video.