Connectedness is closure-preserved

This article gives the statement, and possibly proof, of a topological space property (i.e., connected space) satisfying a topological space metaproperty (i.e., closure-preserved property of topological spaces)
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Statement

Suppose $X$ is a topological space and $A$ is a subset of $X$ that is a connected space with the subspace topology from $X$. Then, the closure of $A$ in $X$, denoted $\overline{A}$, is also a connected space with the subspace topology from $X$.