Prove that a continuous function from a compact metric space to any metric space is closed.

Question

My problem is as stated in the title. Primarily, I am looking for if anyone could give me a hint. It would be very appreciated, I am not seeking after a full proof.

Answer 1

Hint: What can you say about a closed subset of a compact space? Is that property preserved by a continuous map? How do you conclude the image is closed?

Answer 2

Closed subsetst of a compact space are compact. The image of a compact set with respect to a continuous function is continuous. Compact subsetst are closed.