Representing finite convex geometries by relatively convex sets
نویسندگان
چکیده
منابع مشابه
Join-semidistributive Lattices of Relatively Convex Sets
We give two sufficient conditions for the lattice Co(Rn, X) of relatively convex sets of Rn to be join-semidistributive, where X is a finite union of segments. We also prove that every finite lower bounded lattice can be embedded into Co(Rn, X), for a suitable finite subset X of Rn.
متن کاملMinkowski Algebra I: a Convolution Theory of Closed Convex Sets and Relatively Open Convex Sets∗
This is the first one of a series of papers on Minkowski algebra. One of purposes of this paper is to set up a general framework so that the mixed volume theory and integral geometry can be developed algebraically in subsequent papers. The so called Minkowski algebra of convex sets is the vector space generated by indicator functions of closed convex sets and relatively open convex sets, where ...
متن کاملFinite Sets as Complements of Finite Unions of Convex Sets
Suppose S ⊆ R is a set of (finite) cardinality n whose complement can be written as the union of k convex sets. It is perhaps intuitively appealing that when n is large k must also be large. This is true, as is shown here. First the case in which the convex sets must also be open is considered, and in this case a family of examples yields an upper bound, while a simple application of a theorem ...
متن کاملOn a convex operator for finite sets
Let S be a finite set with n elements in a real linear space. Let JS be a set of n intervals in R. We introduce a convex operator co(S,JS) which generalizes the familiar concepts of the convex hull conv S and the affine hull aff S of S. We establish basic properties of this operator. It is proved that each homothet of conv S that is contained in aff S can be obtained using this operator. A vari...
متن کاملFinite Illumination of Unbounded Closed Convex Sets
If K is an unbounded closed convex subset of Ed having nonempty interior, we seek necessary and/or sufficient conditions to ensure that the boundary of K can be externally illuminated from a finite set of directions. This problem was stated as open in a recent book by Boltyanski. The tools used in this search are those developed by Visibility Theory such as the ideas of star, inner stem, visibi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2014
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2013.07.012