Let $f, g: X \rightarrow \mathbb{R}$ be continuous functions, where ($X, \tau$) is a topological space and $\mathbb{R}$ is given the standard topology.
a)Show that the function $f \cdot g : X \rightarrow \mathbb{R}$,defined by $(f \cdot g)(x) = f(x)g(x)$
is continuous.
b)Let $h: X \setminus \{x \in X | g(x) = 0\}\rightarrow \mathbb{R}$ be defined by $h(x) = \frac{f(x)}{g(x)}$
Show that $h$ is continuous.