Suppose $E$ is a topological space, $A$ is a subset of $E$. Card(A) is the cardinal of $A$. $\bar{A}$ is the closure of $A$. Do we have $Card(\bar{A})\le 2^{2^{Card(A)}}$.

Suppose $E$ is a Hausdorff topological space, $A$ is a subset of $E$. Card(A) is the cardinal of $A$. $\bar{A}$ is the closure of $A$. Do we have $Card(\bar{A})\le 2^{2^{Card(A)}}$.