Does anyone have any references about intersections of subspaces with sets (which are NOT subspaces)?
Intersection of subspaces is boring, but if I am given a set $S$ which is not a subspace and some list of subspaces $\mathcal{E}$, what do we known about the $E\in \mathcal{E}$ when $E$ is intersecting $S$.
Any reference would be really helpfull.
UPDATE:
If I have an $n$-dim vector space $V$ over $GF(2)$ and a set $T$ with $|T|\geq \frac{|V|}{2}$, which is NOT a subspace, is there a bound on the number of $k$-dim subspaces $U$ of $V$ intersecting $T$.