pointless topology

English

Noun

pointless topology (usually uncountable, plural pointless topologies)

1. (mathematics) An approach to topology that avoids mentioning points.
   • 1995, Francis Buekenhout, editor, Handbook of Incidence Geometry: Buildings and Foundations, North-Holland: Elsevier, page 1018:

     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.

   • 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

• (approach to topology): locale theory, pointfree topology

Coordinate terms

• point-set topology

Further reading

• Whitehead's point-free geometry on Wikipedia.Wikipedia
• Stone duality on Wikipedia.Wikipedia