Course abstract

Topology is the study of abstract shapes and their properties which do not change under stretching or squeezing an object without tearing. In this course, we shall investigate and formalize the abstract notion of a “space” under a bare minimum set-theoretic structure, called a topology. This basic structure gives rise to a beautiful and rich source of ideas which at the same time greatly simplify and extend familiar objects in mathematics, such as limits and continuous functions. Arguably, topology (along with the theory of numbers) lies at the heart of mathematics. I invite you to explore this abstract yet foundational theory which plays a significant role in modern mathematics, and by extension, other mathematical sciences.