# Myope topology

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A topology on the family $\mathcal{K} = \mathcal{K}_X$ of compact subsets of a topological space $X$, an instance of a "hit-or-miss topology". Let $\mathcal{F}$ denote the family of closed sets in $X$ and $\mathcal{G}$ the family of open sets. A basic open set for the myope topology is a set $U_{F,G} \subset \mathcal{K}$ of the form $$U_{F,G} = \{ A \in \mathcal{K} : A \cap F = \emptyset\,\ A \cap G \ne \emptyset \}$$ where $F \in \mathcal{F}$ and $G \in \mathcal{G}$.