I use the following definition. Let $V$ be a vector space over some field $F$.
Non-empty set $A \subset V$ is called affine set (sometimes affine subspace, linear manifold, linear variety and probably somehow else) iff $$ A = \{x + v ~~|~~ x \in L\} $$ for some linear subspace $L$ of $V$ and some vector $v \in V$.
It's easy to prove that non-empty intersection of any collection of affine sets is an affine set. Thus a question rises: when is the intersection non-empty?
There's a simple criteria for two affine sets: $L_1 + v_1$ and $L_2 + v_2$ have non-empty intersection iff $v1 - v2 \in L_1 + L_2$.
Is there any criteria for collection of more than two affine sets?
Thanks in advance.