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.
- Spanier, E. (1963), "Quasi-topologies", Duke Mathematical Journal, 30 (1): 1–14, doi:10.1215/S0012-7094-63-03001-1, MR 0144300.
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