pointless topology

plural pointless topologies

1. uncountableusuallymathematicsAn approach to topology that avoids mentioning points.

   The works of Ehresmann [1957/58], Benabou [1957/58], Papert and Papert [1957/58] give rise to pointless topology, i.e. an abstract treatment of a class of lattices (the frames) extending the class whose members are the lattices of open sets of the topological spaces.

   1995, Francis Buekenhout, editor, Handbook of Incidence Geometry: Buildings and Foundations, North-Holland: Elsevier, page 1018

   2 more examples

   1997, Stephen C. Hirtle, Andrew U. Frank (editors), Spatial Information Theory A Theoretical Basis for GIS: International Conference COSIT '97, Proceedings, Springer, LNCS 1329, page 170, Pointless topology is more general than point-set topology in that there are complete Heyting algebras which do not come from the open set lattices of topological spaces.

   2001, Peter Johnstone, Elements of the History of Locale Theory, C.E. Aull, R. Lowen (editors), Handbook of the History of General Topology, Volume 3, Kluwer Academic, page 841, Banaschewski was to become one of the most prolific authors on pointless topology, and in particular on its constructive and choice-free aspects, in the next three decades.

   Synonyms: locale theory, pointfree topology