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# Is a restriction of a continuous function always continuous?

From Mathematics Is A Science

Jump to navigationJump to searchQuestion: Is a restriction of a continuous function always continuous?

Answer: Yes.

Why: The full version of the question is: "Is the restriction of a function continuous on a topological space $X$ to a subset $A$ of $X$ continuous with respect to the relative topology on $A$ induced by the topology of $X$?" With that the answer is clear...