Myope topology

2020 Mathematics Subject Classification: Primary: 54B20 Secondary: 54J05 [MSN][ZBL]

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 $G \in \mathcal{G}$.

References

• C. van den Berg, J. P. R. Christensen, P. Ressel, "Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions" Graduate Texts in Mathematics 100 Soringer (2012) ISBN 146121128X