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.
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.
Let f : X → Y be a function such that X and Y are 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.If f : X → Y and g : Y → Z are both quasi-open (such that all spaces are topological), then the function composition h = g ∘ f : X → Z is quasi-open.