Partial linear space
Encyclopedia
A partial linear space is a basic incidence structure
in the field of incidence geometry, that carries slightly less structure than a linear space
.
an incidence structure, for which the elements of 
are called points and the elements of 
are called lines. S is a partial linear space, if the following axioms hold:
Incidence structure
In mathematics, an incidence structure is a tripleC=.\,where P is a set of "points", L is a set of "lines" and I \subseteq P \times L is the incidence relation. The elements of I are called flags. If \in I,...
in the field of incidence geometry, that carries slightly less structure than a linear space
Linear space (geometry)
A linear space is a basic structure in incidence geometry. It consists of a family of subsets of a set such that the intersection of two subsets contains at most one element of the set...
.
Definition
Let an incidence structure, for which the elements of are called points and the elements of are called lines. S is a partial linear space, if the following axioms hold:
- any line is at least incident with two points
- any pair of distinct points is incident with at most one line
External links
- partial linear space at a website of the university of Kiel
- partial linear space at PlanetMathPlanetMathPlanetMath is a free, collaborative, online mathematics encyclopedia. The emphasis is on rigour, openness, pedagogy, real-time content, interlinked content, and also community of about 24,000 people with various maths interests. Intended to be comprehensive, the project is hosted by the Digital...