# Properties of Continuous Function

• October 8th 2010, 01:20 AM
saaya
Properties of Continuous Function
I am completely lost for the following question. Can someone help?

If http://data.artofproblemsolving.com/...4c16f1baa6.gif is continuous and A is a bounded subset of http://data.artofproblemsolving.com/...6c599776c2.gif, prove that http://data.artofproblemsolving.com/...51a3384683.gif. Is this necessarily true if A is not bounded?
• October 8th 2010, 08:31 PM
Tinyboss
What if $A$ is all of $\mathbb{R}^p$? What's $\overline{A}$? What if $F(A)$ is open and not all of $\mathbb{R}^p$?