Point-Set Topology Lecture Series on Mandelcord

This post is to announce that there will be a lecture course on General Topology (a.k.a. Point-Set Topology) conducted in Mandelcord (the blue math discord server). Everyone is invited to join: discord.gg/maths . If any of you were present in the Real Analysis lecture course during the summer, you know what I'm talking about, and you might be pleased to hear that this course will also be run by Pear Category Theorem (the same person). Why YOU should do topology Point-set topology is one of the most important subjects that you learn, and mastering topological thinking is as important a milestone as learning to write a proof. This is a good subject to study alongside measure theory, or simply by itself after one has learned analysis or algebra. Course Structure The course will primarily follow the flow of the first half of Munkres. The plan is to go through all 8 chapters, spending maybe one to two weeks on each chapter, aiming for an approximately 16 week course. Also the instructor intends to supplement the book with his own intuition on the subject, as well as connections to other subjects that he thinks are of interest and possibly also other topics not covered in the book. Many examples of various pathological properties will be provided. The study of metric spaces and functions on them will be paramount; but where Rudin introduces metric spaces as merely a generalization of Euclidean spaces, we will explore just how pathological these spaces can be, or else what properties they must have. The instructor also plans to put far more focus on the topics of topological groups and nets than Munkres does. Topological groups, because often in "the real world" we do not care about a topological space by itself, but rather some other more complicated structure given a topology, in order to see what the topology can tell you about the thing itself; topological groups provide a playground to learn that mode of thinking. Nets are also very important; where sequences are of importance in R , they can only tell you so much in general topological spaces, so nets therefore become the natural way to recover theorems about sequences. Material and References Topology - Munkres Counterexamples in Topology - Steen & Seebach Timeline The course starts with the first lecture on 17th November at 9 PM CET ( 20:00 UTC ), with subsequent lectures on Tuesdays and Thursdays . Lectures will be recorded and posted promptly. Prerequisites/Who can join? Everyone. It is completely free for anyone who wants to join. Just click the link and join the server: you can find the channel called topology-course in the section called General maths . As for prerequisites, a first course in Real Analysis and Group Theory is sufficent. Looking forward to see all of you there. Thank you.