Regular Functions on Quasi-Affine Varieties

This lecture delves into the concept of regular functions on quasi-affine varieties, exploring how they allow the definition of morphisms, local rings, and rational functions. The instructor illustrates this with motivating examples and explains the definition of regular functions on quasi-affine varieties. The lecture also covers the relationship between regular functions and continuous functions, proving that regular functions are continuous. Furthermore, the lecture discusses the importance of regular functions in defining algebraic varieties and introduces the notion of sheaves. It concludes by highlighting the construction of quotient fields and local rings for quasi-affine varieties, emphasizing their similarities with those for affine varieties.