Topological intersection theorems
J{ürgen Kindler · Proceedings of the American Mathematical Society · 1993
Let $\{ {C_x}:x \in X\}$ be a family of subsets of some set $Y$. A purely topological condition is given that is both necessary and sufficient for $\bigcap {\{ {C_x}:x \in X\} }$ to be nonvoid. Applications to minimax theorems are sketched.