Category:Geometric transversal theory
{{JEL code|C65}}
{{Cat main|Helly's theorem}}
{{See also|Carathéodory's theorem (convex hull)|Radon's theorem}}
{{MSC|id=52A35|title=Helly-type theorems and geometric transversal theory}}
In mathematics, geometrical transversal theory is a subfield of convex and discrete geometry that studies the intersections of classes of sets. Classical geometrical transversal theory studies the class of convex sets. Contemporary geometric transversal theory considers also more general sets, which have been studied with algebraic topology.{{cite journal|mr=1218037|last=Chichilnisky|first=G.|authorlink=Graciela Chichilnisky|title=Intersecting families of sets and the topology of cones in economics|journal=Bulletin of the American Mathematical Society (New Series)|volume=29|year=1993|number=2|pages=189–207|doi=10.1090/S0273-0979-1993-00439-7|arxiv=math/9310228|bibcode=1993math.....10228C|url=http://www.ams.org/journals/bull/1993-29-02/S0273-0979-1993-00439-7/S0273-0979-1993-00439-7.pdf}}
References
- {{citation
| last1 = Danzer | first1 = L.
| last2 = Grünbaum | first2 = B. | author2-link = Branko Grünbaum
| last3 = Klee | first3 = V. | author3-link = Victor Klee
| contribution = Helly's theorem and its relatives
| pages = 101–179
| publisher = American Mathematical Society
| series = Proc. Symp. Pure Math.
| title = Convexity
| url =
| volume = 7
| year = 1963}}.
- {{citation
| last = Eckhoff | first = J.
| contribution = Helly, Radon, and Carathéodory type theorems
| location = Amsterdam
| pages = 389–448
| publisher = North-Holland
| title = Handbook of Convex Geometry
| volume = A, B
| year = 1993}}.