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.
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.
- If is open, then is quasi-open.
- If is a local homeomorphism, then is quasi-open.
- If and are both quasi-open (such that all spaces are topological), then the function composition is quasi-open.
- Kim, Jae Woon (1998). "A Note on Quasi-Open Maps" (pdf). Journal of the Korean Mathematical Society. B: The Pure and Applied Mathematics. 5 (1): 1–3. Retrieved October 20, 2011.
- Blokh, A.; Oversteegen, L.; Tymchatyn, E.D. (2006). "On almost one-to-one maps". Trans. Amer. Math. Soc.
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