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In mathematics, particularly in topology, a set \( A \) is referred to as a **dense set** in a space \( X \) if every point in \( X \) is either an element of \( A \) or is arbitrarily close to a point in \( A \). More formally, a subset \( A \) of a topological space \( X \) is dense in \( X \) if the closure of \( A \) is equal to \( X \).