Fell topology

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The Fell topology on $\mathrm{CL}(X)$ can be regarded as a hit-and-miss topology with subbase $$\{U^- \colon U \in \tau\} \bigcup \{V^+ \colon X \setminus V \mathrm{\hspace{2pt} is \hspace{2pt} compact}\}.$$

References

Beer, Gerald ; Tamaki, Robert K. On hit-and-miss hyperspace topologies. Comment. Math. Univ. Carolin. 34 (1993), no. 4, 717--728.