# Math Help - Properties of Continuous Function

1. ## Properties of Continuous Function

I am completely lost for the following question. Can someone help?

If is continuous and A is a bounded subset of , prove that . Is this necessarily true if A is not bounded?

2. What if $A$ is all of $\mathbb{R}^p$? What's $\overline{A}$? What if $F(A)$ is open and not all of $\mathbb{R}^p$?