My original proof of “continuous mappings on compact metric spaces are uniformly continuous”

The proof of “continuous mappings on compact metric spaces are uniformly continuous” is rather convoluted and opaque, as given in most real analysis textbooks (Rudin included). There is a lot of unnecessary bookkeeping, and the treatment is not really motivated. Given below is my own proof of the theorem, which is inspired by the existingContinue reading “My original proof of “continuous mappings on compact metric spaces are uniformly continuous””