Editing Convex set (section)

=== Intersections and unions ===
The collection of convex subsets of a vector space, an affine space, or a [[Euclidean space]]  has the following properties:<ref name="Soltan" >Soltan, Valeriu, ''Introduction to the Axiomatic Theory of Convexity'', Ştiinţa, [[Chişinău]], 1984 (in Russian).
</ref><ref name="Singer" >{{cite book|last=Singer|first=Ivan|title=Abstract convex analysis|series=Canadian Mathematical Society series of monographs and advanced texts|publisher=John Wiley&nbsp;&&nbsp;Sons, Inc.|location=New&nbsp;York|year= 1997|pages=xxii+491|isbn=0-471-16015-6|mr=1461544}}</ref>
#The [[empty set]] and the whole space are convex.
#The intersection of any collection of convex sets is convex.
#The ''[[union (sets)|union]]'' of a collection of convex sets is convex if those sets form a [[Total order#Chains|chain]] (a totally ordered set) under inclusion. For this property, the restriction to chains is important, as the union of two convex sets need not be convex.