- Let f =
. Show f is continuous at every point t.
≤ K where
K is a constant. Show that f
is everywhere continuous. Functions satisfying such an inequality are called
α where K is a constant and α ∈.
f is everywhere continuous.
- Suppose f : F3 → F is given by f = 3
x1x2 + 2x32. Use Theorem 5.3.2 to
verify that f is continuous. Hint: You should first verify that the function,
πk : F3 → F given by πk =
xk is a continuous function.
- Generalize the previous problem to the case where f : Fq → F is a polynomial.
- State and prove a theorem which involves quotients of functions encountered
in the previous problem.