Abstract
Abstract For any m = −1,0,1,2,... ,n, a subspace of dimension m, or m-space, of PG(n, K) is a set of points all of whose representing vectors form, together with the zero, a subspace of dimension m+1 of V = V(n 4+1, q); it is denoted by Πm A subspace of dimension zero has already been called a point; a subspace of dimension −1 is the empty set. Subspaces of dimension one, two, three are respectively a line, a plane, a solid. A subspace of dimension n −1 is a prime or hyperplane-, a subspace of dimension n−2 is a secundum. A subspace of dimension n −r is also referred to as a subspace of codimension r. The set of m-spaces is denoted PG(m)(n,q).
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