This repository contains the source code for the book "Topology: An introductory course to the theory of sets and spaces".
This book is a collection of notes that I have been gathering over the years, ever since I was an undergraduate student at the University of Seville, Spain. The notes were originally written in Spanish, but I have been translating them to English since 2020.
The content of this book is intended to serve as an introductory guide for the rigorous self-study of topology. It has been the goal of this project for myself, and now I hope it can be useful for others as well.
When facing the challenge of having to self-study a matter as arduous as Topology, I often found myself lost in books which skipped too many proofs, or too many details of them, which are only trivial (as they are claimed to be) for the experienced reader. In my personal experience, I found this fact to be very discouraging (not only in the case of Topology, but in many other subjects as well). This is why I decided to write my notes in a way that I would have liked to find them when I was a student, and I hope that they can be useful for others as well. I know these notes are not original, in the sense that they are not offering new content to the subject itself. However, I believe these notes (in the form of a book) offer a self-contained and complete guide to the self-study without the need to consult any other sources for the proofs of the results here presented.
The tentative table of contents of this book is the following:
- Topological spaces
- Uniform spaces
- Connectivity
- Compactness
- Countability and separation axioms
- Polish spaces
- Compactification
- Cardinal invariants
- Metric spaces
- Topological groups
- Vector spaces
- Ordered spaces
The book is written in LaTeX, and the source code is available in this repository. The book is divided into chapters, each of which is a separate LaTeX file. The main file is topology.tex, which contains the preamble and the structure of the book.
This repository comes with the convenience of a Makefile which allows to compile the book with a single command. To see the commands avaliable, run make help in the root directory of the repository.
If you find any typos, errors, or you think there is something that can be improved, please feel free to open an issue or a pull request. I will be happy to review it and merge it into the main branch.