# What is the dimension of disk algebra?

Consider the disk algebra $$A(D)$$ of the analytic functions in the open unit disk $$D$$ that are continuous in $$\overline D$$.

I'm trying to see if the dimension of $$A(D)$$ as a complex vector space is $$\mathfrak{c}$$.

For a theorem we have that the dimension of all Banach space is greater than $$\mathfrak{c}$$.

Well, we have that $$\mathbb C[z]$$ is dense in $$A(D)$$ with the supremum norm in $$\overline D$$ and $$\dim \mathbb C[z] = \aleph_0$$.

There are references of results that implies in the dimension of $$A(D)$$ to be $$\mathfrak c$$?