Summary
We provide a unified approach to three fundamental properties of continuous functions on closed and bounded intervals: the intermediate value theorem, and the uniform continuity theorem. We prove all three using the same building block, only making use of the least upper bound axiom and the definition of continuity.
Additional information
Notes on contributors
Daniel Daners
Daniel Daners (MR Author ID: 325132) grew up in Switzerland. He studied and obtained a Ph.D. at the University of Zürich in 1992. After a number of postdoctoral years in various places he finally settled with his family in Australia, teaching at the University of Sydney.