Given a topological space (S,\tau) and a subset X of S, the topology \tau(x) = ≤ft{A \cup (A' ∩ X)/A,A' ∈ τ \right} is called the simple extension of \tau by X (see Levine 3).Here we show how to recognize when two subsets X and Y of S define the same simple extension of \tau and we give a characterization of those expansions of \tau which are simple extensions of \tau by suitable subsets of S.

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