The Heine-Cantor theorem states that a continuous function from a compact metric space to a metric space is uniformly continuous. In particular, every real-valued function on a bounded closed interval that is continuous is uniformly continuous.
Heine-Cantor Theorem
See also
Compact Space, Continuous Function, Heine-Borel Theorem, Uniformly ContinuousExplore with Wolfram|Alpha
References
Rudin, W. Principles of Mathematical Analysis, 3rd ed. New York: McGraw-Hill, 1976.Cite this as:
Weisstein, Eric W. "Heine-Cantor Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Heine-CantorTheorem.html