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* The three diagonal points of a [[complete quadrangle]] are never collinear.
{{anchor|Projective subspace}}A '''subspace''' of the projective space is a subset ''X'', such that any line containing two points of ''X'' is a subset of ''X'' (that is, completely contained in ''X''). The full space and the empty space are
The geometric dimension of the space is said to be ''n'' if that is the largest number for which there is a strictly ascending chain of subspaces of this form:
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