Question 1
Which set is a vector space over $\mathbb{R}$ under pointwise addition and scalar multiplication?
Question 2
What is $\|f\|_\infty$ for $f(x)=x(1-x)$ on $[0,1]$?
Question 3
If $f_n\to f$ uniformly on $[a,b]$ and each $f_n$ is continuous, what can be concluded about $f$?
Question 4
Which statement best describes pointwise convergence of $f_n$ to $f$ on a set $X$?
Question 5
Which space is complete under the sup norm $\|\cdot\|_\infty$?
