Quasitopological space

In mathematics, a quasi-topology on a set "X" is a function that associates to every compact Hausdorff space "C" a collection of mappings from "C" to "X" satisfying certain natural conditions. A set with a quasi-topology is called a quasitopological space

They were introduced by Spanier, who showed that there is a natural quasi-topology on the space of continuous maps from one space to another.

References

* Spanier, E. "Quasi-topologies." Duke Math. J. 30 1963 1-14.