View source for Category:Geometric transversal theory

{{JEL code|[[JEL classification codes#Mathematical and quantitative methods JEL: C Subcategories|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 geometry|convex]] and [[discrete geometry]] that studies the [[intersection (set theory)|intersections]] of classes of sets. Classical geometrical&nbsp;transversal theory studies the class of [[convex set]]s. Contemporary geometric&nbsp;transversal theory considers also more general sets, which have been studied with [[algebraic topology]].<ref>{{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}}</ref>

==References==
<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}}.

[[Category:Convex geometry]]
[[Category:Discrete geometry]]
[[Category:Matroid theory]]
[[Category:Ramsey theory]]
[[Category:Convex hulls]]
[[Category:Families of sets]]
[[Category:Geometric intersection]]