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.[1]
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.[1][2]
Properties
Let be a map between topological spaces.
See also
- Almost open map – Map that satisfies a condition similar to that of being an open map.
- Closed graph – Graph of a map closed in the product space
- Closed linear operator – Graph of a map closed in the product space
- Open and closed maps – A function that sends open (resp. closed) subsets to open (resp. closed) subsets
- Proper map – Map between topological spaces with the property that the preimage of every compact is compact
- Quotient map (topology) – Topological space construction