pointless topology
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English
Noun
pointless topology (usually uncountable, plural pointless topologies)
- (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
Further reading
Whitehead's point-free geometry on Wikipedia.Wikipedia - Stone duality on Wikipedia.Wikipedia
