Geodesic
Hyperspace of the $\Pi$-complete spaces and maps
Eurasian mathematical journal, Tome 12 (2021) no. 2, pp. 104-110

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In the present paper we establish that the space $\exp_\beta X$ of compact subsets of a Tychonoff space $X$ is $\Pi$-complete if and only if $X$ is so. Further, we prove the Tychonoff map $\exp_\beta f: \exp_\beta X\to \exp_\beta Y$ is $\Pi$-complete if and only if a given map $f: X\to Y$ is $\Pi$-complete. 
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     title = {Hyperspace of the $\Pi$-complete spaces and maps},
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A. A. Zaitov; D. I. Jumaev. Hyperspace of the $\Pi$-complete spaces and maps. Eurasian mathematical journal, Tome 12 (2021) no. 2, pp. 104-110. http://geodesic.mathdoc.fr/item/EMJ_2021_12_2_a10/