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 f : X \to Y between topological spaces X and Y is quasi-open if, for any non-empty open set U \subset X, the interior of f(U) in Y is non-empty.[1][2]

Properties

Let f: X \to Y be a function such that X and Y are topological spaces.

References

  1. 1 2 3 4 5 6 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.
  2. Blokh, A.; Oversteegen, L.; Tymchatyn, E.D. (2006). "On almost one-to-one maps". Trans. Amer. Math. Soc.


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