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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

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The cardinal of the closure of a set in a topological space

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 $Card(\bar{A})\le 2^{2^{Card(A)}}$.
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