README

Until further notice, the information and lectures for MAT3500/4500 will be given in English.

"Topos" means "place", so "Topology" is the science of places, or the study of shapes, if you like.  The main objects of study are shapes where we can make sense of limits, known as topological spaces.  We can also make sense of what it means for a function from one such shape to another to be continuous.  A large part of the course is about the properties of continuous functions, which we call maps.  A second large part of the course is concerned with the properties of shapes that are invariant under invertible continuous transformations.  For brief historical notes on the subject you may with to look at these excerpts from the Bourbaki volume on General Topology. (If you have not heard of Nicolas Bourbaki, do a web search now.)

We will follow James Munkres' textbook "Topology" (in its Pearson New International Edition/Second Edition).  This international edition unfortunately has a poor table of contents (on page 1), and a really poor index (on pages 501-503).  A refined table of contents will be maintained here.  The order of chapters 12 and 13 has also been reversed, but that will not affect this course.

The core material for MAT3500/4500 starts in chapter 2.  The preliminary chapter 1, on "Set theory and logic", is a mixed bag of elementary notation and some fairly sophisticated material, partially going beyond our needs.  I will therefore only go through some of the sections of chapter 1, as needed for the later chapters. I also plan to skip Section 14, as the order topologies mainly serve as a source of counterexamples. Here are my lecture notes from the last time I taught this course.  They may get updated as we go along.