I need to tell if this space/set is compact in $C[0,1]$
$x_n(t) = t^n, n ∈ N$
Following Arzelà–Ascoli theorem, the set is compact when it has Uniform boundedness and Equicontinuity, is it correct?
So Uniform boundedness, in my case:
$Ǝ M: ∀φ(t)∈Q=>|φ(t)|≤M,∀t∈[0,1]$
But I'm really confused whether it's correct or not, or how to solve this overall