X and Y are topological spaces. $\displaystyle f:X\to Y$ is said to be open if for every open set $\displaystyle U$ of $\displaystyle X$, the set $\displaystyle f(U)$ is an open set of Y. Show projections $\displaystyle \pi_1=X\times Y\to X$ and $\displaystyle \pi_2=X\times Y\to Y$ are open maps.

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