Thread: 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.

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.

What is the relationship between

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