Quasi-interior

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In topology, a continuous map f : X \rightarrow Y between topological spaces X and Y is said to be quasi-interior if, for any open set U \subset X, the interior of f(U) in Y is non-empty.

[edit] References

A.Blokh, L.Oversteegen and E.D.Tymchatyn, "On almost one-to-one maps", Trans. Amer. Math. Soc (2006).