Quasi-open map

In topology a branch of mathematics, a quasi-open map or quasi-interior map is a function which has similar properties to continuous maps. However, continuous maps and quasi-open maps are not related.

Definition
A function $f : X → Y$ between topological spaces $X$ and $Y$ is quasi-open if, for any non-empty open set $U ⊆ X$, the interior of $f ('U)$ in $Y$ is non-empty.

Properties
Let $$f:X\to Y$$ be a map between topological spaces.
 * If $$f$$ is continuous, it need not be quasi-open. Conversely if $$f$$ is quasi-open, it need not be continuous.
 * If $$f$$ is open, then $$f$$ is quasi-open.
 * If $$f$$ is a local homeomorphism, then $$f$$ is quasi-open.
 * The composition of two quasi-open maps is again quasi-open.