# Continuity of the restriction of a function to a set

Let $$X$$ be a topological space and $$f$$ a real-valued function defined on $$X$$. Let $$S\subset X$$ and suppose $$f$$ is continuous with respect to the induced topology on $$S$$ (opens are in the form $$S\cap V$$, where $$V$$ is an open of $$X$$). Is this the same as saying that the restriction of $$f$$ to $$S$$ is continuous?