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In the work, it is established that the space of all nonempty compact subsets of a Tychonoff space is (O-C)–compact if and only if the give Tychonoff space is (O-C)–compact. Further, for a map f:X→Y the map expβX→Y is (O-C)–compact if and only if the map f is (O-C)–compact.

(O-C)-compact Spaces and Hyperspaces Functor