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Suppose that $C$ is locally direct product, that is, for any $(a,b)\\in X\\times Y$, there exist an open set $U$ of $X$, an open set $V$ of $Y$, a subset $I$ of $U$ and a subset $J$ of $V$ such that $(a,b) \\in U\\times V$ and $$C\\cap (U\\times V)=I\\times J$$ hold. Then, in this memo, we show that $C$ is globally so, that is, there exist a subset $A$ of $X$ and a subset $B$ of $Y$ such that $$C=A\\times B$$ holds. The proof is elementary. 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