Topic
Separoid
About: Separoid is a research topic. Over the lifetime, 4 publications have been published within this topic receiving 96 citations.
Papers
TL;DR: It is shown how the concept of separoid unifies a variety of notions of ‘irrelevance’ arising out of different formalisms for representing uncertainty in Probability, Statistics, Artificial Intelligence, and other fields.
Abstract: We introduce an axiomatic definition of a mathematical structure that we term a i>separoid. We develop some general mathematical properties of separoids and related axiom systems, as well as connections with other mathematical structures, such as distributive lattices, Hilbert spaces, and graphs. And we show, by means of a detailed account of a number of models of the separoid axioms, how the concept of separoid unifies a variety of notions of ‘irrelevance’ arising out of different formalisms for representing uncertainty in Probability, Statistics, Artificial Intelligence, and other fields.
98 citations
TL;DR: A Borsuk—Ulam-type theorem is proved which has as a corollary a generalization of Hadwiger’s theorem the topological notion of virtual transversal.
Abstract: In this paper we study the topology of transversals to a family of convex sets as a subset of a Grassmanian manifold. This topology seems to be ruled by a combinatorial structure which we call a separoid. With these combinatorial objects and the topological notion of virtual transversal we prove a Borsuk--Ulam-type theorem which has as a corollary a generalization of Hadwiger's theorem.
22 citations
1 Jan 2002
TL;DR: In this article, the geometric dimension of an oriented matroid is introduced, which is the minimal euclidian dimension where its separoid (to be defined) can be realized as a family of convex sets.
Abstract: In this paper the geometric dimension of an oriented matroid is introduced. It is the minimal euclidian dimension where its separoid (to be defined) can be realized as a family of convex sets. We show that in the uniform case, it is enough to know this invariant to decide if the oriented matroid is linear.
4 citations
TL;DR: It will be showed here that, when restricted to point separoids, there is no finite duality.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2007 | 1 |
| 2002 | 2 |
| 2001 | 1 |