摘要
设S=(P,L)是点正则的阶为t≥2的空间,即为过每点有t+1条线的线性空间,|P|=v=t2+t,L=b=v+1,并设|Vi-Vi|≤1,max{V1……Vb,}=t+1,则线性空间S必为穿孔的射影平面;反之,t≥2阶射影平面的穿孔必为点正则的阶为t的线性空间,而且|P|=v=t2+t,|L|=v+1,|vi-vj|≤1。
Let S = (P. L) be a finite linear space with V points and blines.Then, S is a punctured projective plane with the order of t>2, if and only if S is pointregular with an order t>2, |p|=v=t2+t, |L|=b=v+1, |vi-vj|<1 (i,j= 1, 2,... b)and max{v1,v2..vb} =t+1.