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Which of the following are always continuous for any topological spaces $X$ and $Y$ and any continuous function $f:X\rightarrow Y$? Select ALL that apply.

A

The function obtained by restricting the domain of $f$.

B

The function obtained by restricting the range of $f$ to a subspace containing $f(X)$.

C

The function obtained by extending the domain of $f$.

D

The function obtained by extending the range of $f$.

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