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Proposition: Bijective Open Functions
Let $(X,\mathcal O_X)$ and $(Y,\mathcal O_Y)$ be topological spaces. A bijective function $f:X\to Y$ is an open function if and only if its inverse function is continuous.
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References
Bibliography
 Steen, L.A.;Seebach J.A.Jr.: "Counterexamples in Topology", Dover Publications, Inc, 1970
 Jänich, Klaus: "Topologie", Springer, 2001, 7th Edition