Topological intersection theorems

Kindler, Jürgen

doi:10.1090/S0002-9939-1993-1127141-4

Topological intersection theorems
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by Jürgen Kindler

Proc. Amer. Math. Soc. 117 (1993), 1003-1011

DOI: https://doi.org/10.1090/S0002-9939-1993-1127141-4

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Abstract:

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.

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