Unified Proofs of Three Fundamental Properties of Continuous Functions

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 $ϵ-\delta$ definition of continuity.

MSC::

• Primary 26A15
• Secondary 26A06

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.