prove that if T is closed then the inverse image is closed

Let f : R → R be a continuous function and let S ⊆ R and T ⊆ R. How do I prove that:

If T is closed, then f−1(T) is closed.

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Originally Posted by alice8675309

Let f : R → R be a continuous function and let S ⊆ R and T ⊆ R. How do I prove that: If T is closed, then f−1(T) is closed.

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What is the relationship between http://quicklatex.com/cache3/ql_27fc...9828f09_l3.png

To give a complete answer, one would have to know what definition of "closed" you are using (there are several different, but equivalent, definitions).