Homework 11: Continuity

1. Section 4.1, #4.9, 4.10, 4.12, 4.13(a), 4.14.
2. Let \(f,g:X\to \bR\) be continuous, where \(\bR\) is given the standard topology.
   1. Prove that \(\{x:f(x)\leq g(x)\}\) is closed in \(X\).
   2. Let \(h:X\to\bR\) be the function \(h(x)=\min\{f(x),g(x)\}\). Prove that \(h\) is continuous. (Hint: use the pasting lemma.)