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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 $\mathfrak c$?

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