In topology, a **scattered space** is defined as a topological space in which there are no non-empty subsets that are dense in the space. More formally, a topological space \( X \) is called scattered if every non-empty subset \( A \) of \( X \) contains a point \( x \) such that the closure of \( \{x\} \) in \( X \) does not include any other points of \( A \).
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