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Consider a Henselian rank one valued field $K$ of equicharacteristic zeroalong with the language $\mathcal{L}^{P}$ of Denef--Pas. Let $f: A \to K$ be an$\mathcal{L}^{P}$-definable (with parameters) function on a subset $A$ of$K^{n}$. We prove that $f$ is piecewise continuous; more precisely, there is afinite partition of $A$ into $\mathcal{L}^{P}$-definable locally closed subsets$A_{1},\ldots,A_{s}$ of $K^{n}$ such that the restriction of $f$ to each$A_{i}$ is a continuous function.

Piecewise continuity of functions definable over Henselian rank one valued fields