In Pointless Topology - known by serious people as Pointfree Topology - a change of perspective to regular point-set topology is done, shifting the focus from the points in the space to its collection of open sets.

In the first part of the talk, we will motivate this new point of view, describe what it means to "focus on open sets" and investigate in what situations we are able to recover points back from the information in the collection of open sets.

In the second part of the talk, we will see a counterexample by johnstone, originally published in a paper that this talk is named after. In the process, we will introduce Scott (the topology), and learn how to tell a sober topology apart from one that's seeing double!