The space of continuous functions vanishing at infinity \(C_0(X)\) is a Banach space .
Proof
The space \(C_0(X)\) is a closed subspace of \(C^b(X)\)
and the space of bounded functions on \(X\) is a Banach space
.
Due to (0x67c55fbe)
\(C_0(X)\) is complete and therefore a Banach space.