About this document
Understanding Continuity in Functions by TOM DAVIS is a document available to read on EtoBox.
This document defines and discusses continuity in metric spaces and topological spaces. It begins by defining continuity using the ε-δ definition. It then proves several properties of continuous functions, including that continuous functions map connected sets to connected sets and compact sets to compact sets. It also defines uniformly continuous and Lipschitz functions. The document concludes by proving several corollaries about continuous functions on compact domains, including the intermediate value the
- Author
- TOM DAVIS
- Language
- EN