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.[1]
Definition
A function between topological spaces and is quasi-open if, for any non-empty open set , the interior of in is non-empty.[1][2]
Properties
Let be a function such that X and Y are topological spaces.
- If is continuous, it need not be quasi-open. Conversely if is quasi-open, it need not be continuous.[1]
- If is open, then is quasi-open.[1]
- If is a local homeomorphism, then is quasi-open.[1]
- If and are both quasi-open (such that all spaces are topological), then the function composition is quasi-open.[1]
References
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