Editing Pointless topology (section)

== History ==
The first approaches to topology were geometrical, where one started from [[Euclidean space]] and patched things together. But [[Marshall Stone]]'s work on [[Stone duality]] in the 1930s showed that topology can be viewed from an algebraic point of view (lattice-theoretic). [[Karl Menger]] was an early pioneer in the field, and his work on topology without points was inspired by [[Whitehead's point-free geometry]] and used shrinking regions of the plain to simulate points.<ref>Menger, Karl "Topology without points." Rice Institute Pamphlet - Rice University Studies, 27, no. 1 (1940) Rice University [https://repository.rice.edu/items/aa654487-128a-4379-9108-9ed1b798e01b]</ref>

Apart from Stone, [[Henry Wallman]] also exploited this idea. Others continued this path till [[Charles Ehresmann]] and his student [[Jean Bénabou]] (and simultaneously others), took a major step in the late fifties. Their insights arose from the study of "topological" and "differentiable" [[Category (mathematics)|categories]].{{sfn|Johnstone|1983|p=42}}

Ehresmann's approach involved using a category whose objects were [[Complete lattice|complete lattices]] which satisfied a [[Distributive property|distributive]] law and whose [[morphism]]s were maps which preserved finite [[Join and meet|meets]] and arbitrary [[Join and meet|joins]]. He called such lattices "local lattices"; today they are called "frames" to avoid ambiguity with other notions in [[lattice theory]].{{sfn|Johnstone|1983|p=43}}

The theory of [[frames and locales]] in the contemporary sense was developed through the following decades ([[John R. Isbell|John Isbell]], [[Peter Johnstone (mathematician)|Peter Johnstone]], Harold Simmons, [[:de:Bernhard Banaschewski|Bernhard Banaschewski]], [[:cs:Aleš Pultr|Aleš Pultr]], Till Plewe, Japie Vermeulen, [[Steve Vickers (computer scientist)|Steve Vickers]]) into a lively branch of topology, with application in various fields, in particular also in theoretical computer science. For more on the history of locale theory see Johnstone's overview.<ref>Peter T. Johnstone, Elements of the history of locale theory, in: Handbook of the History of General Topology, vol. 3, pp. 835-851, Springer, {{ISBN|978-0-7923-6970-7}}, 2001.</ref>