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→More precise definition: add topological definition of continuous function
A continuous function maps a [[compact space]] to a [[compact space]].
A continuous function maps a [[compact space]] to a [[compact space]].
=== Topological definition ===
Let <math>X</math> and <math>Y</math> be [[topological space]]s. A function <math>f\colon X \to Y</math> is continuous if for every set <math>U</math> that is open in <math>Y</math>, the preimage <math>f^{-1}(U)</math> is an open set in <math>X</math>.
=== Metric Spaces ===
=== Metric Spaces ===