Pointless Topology Text What's a good textbook I can use to learn more about pointless topology?  Will I need more than a course in regular, old point-set topology and an algebra course which included some category theory to understand the subject?
 A: If you want to get a quick overview of what pointfree topology is about, I suggest you the following two papers


*

*Picado, Pultr, Tozzi: Locales, link

*Johnstone: The point of pointless topology.
Then, the standard textbooks are the following three and you should probably pick one based on your applications:


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*Johnstone: Stone spaces (1986) -- for a duality-theory oriented introduction to frames/locales.

*Vickers: Topology via logic (1996) -- for the relations with
computer science and logic.

*Pultr, Picado: Frames and Locales - topology without points (2011) -- for the more classical, topology oriented approach.


(I studied frame theory from the last one.)
For your second question, I think that you can comfortably start studying those books if


*

*You know basics of point-set topology, e.g. what's in Kelley: General Topology.

*Then, you will need to know basic category theory. For the most part you will only need to understand what is an adjunction and dual equivalence of categories. (You will need more if you read Johnstone's Stone spaces. But Johnstone gives an overview of the required category theory at the beginning.)

*From order theory, you need to be familiar with Galois adjunctions and complete lattices. Of course that more you know about lattices the better but you will learn what you need on the way.

