Editing Projective space (section)

=== Classification ===
* Dimension 0 (no lines): The space is a single point.
* Dimension 1 (exactly one line): All points lie on the unique line.
* Dimension 2: There are at least 2 lines, and any two lines meet. A projective space for {{math|1=''n'' = 2}} is equivalent to a [[projective plane]].  These are much harder to classify, as not all of them are isomorphic with a {{math|PG(''d'', ''K'')}}. The [[Desarguesian plane]]s (those that are isomorphic with a {{math|PG(2, ''K''))}} satisfy [[Desargues's theorem]] and are projective planes over division rings, but there are many [[non-Desarguesian plane]]s.
* Dimension at least 3: Two non-intersecting lines exist. {{harvtxt|Veblen|Young|1965}} proved the [[Veblen–Young theorem]], to the effect that every projective space of dimension {{math|''n'' ≥ 3}} is isomorphic with a {{math|PG(''n'', ''K'')}}, the {{math|''n''}}-dimensional projective space over some [[division ring]]&nbsp;{{math|''K''}}.