Topology Notes

Introduction

These notes were taken by Kyle Dituro in the Fall semester of 2023 at Tufts University. The course was taught by Sebastian Bozlee at the undergraduate level. The intended textbook for the course is Topology Second Edition by James R. Munkres.

I probably forgot to spell-check most of these documents, and some of them are liable to have blatant errors in them.

This repo includes LaTeX files, including my personal header file used to typeset these notes. If you have any questions about this header file, I probably can’t answer them even though I wrote the damn thing, but I’ll sure give it a try.

The TeX was done in Emacs with auctex and latex-preview-pane, and a very very strange header. While my header might be good for sourcing some useful packages and keystroke-saving user defined functions, I highly recommend developing your own LaTeX header over time such that you really get a sense of how LaTeX works.

List of Topics and Dates

Month	Date	Topic
Feb	23.02.10	Real Continuity
	23.02.14	Real Continuity and Topology Def
	23.02.17	Topology Def, Open sets, and Topological Continuity
	23.02.21	Closed sets and the Zariski Topology
	23.02.24	The Subspace Topology and Bases
	23.02.28	Bases
Mar	23.03.01	Universal Props, Limit points, and Adherent points
	23.03.07	Homeomorphisms
	23.03.10	Subbases and the Product Topology
	23.03.14	More on the Product Topology
	23.03.28	Interior and Closure
	23.03.29	Local Continuity and Restrictions
	23.03.31	The Sheaf Property
Apr	23.04.04	The Quotient Topology
	23.04.07	More about the Quotient Topology
	23.04.11	Quotients, Gluing, and Manifolds
	23.04.12	Connectedness
	23.04.14	Convexity, Connectedness, and Path Connectedness
	23.04.18	Connected Components, Open Covers, and Subcovers
	23.04.25	Compactness and Hausdorff-ness
	23.04.26	The Tube Lemma and Compact Subsets in R
	23.04.28	Boundedness, The Extreme Value Theorem and Algabraic Geometry