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Could someone please edit this article to define "compact-valued correspondence" and the meaning of the double-arrow-point??? Otherwise the article is just technobabble. 98.155.236.135 ( talk) 19:06, 28 July 2014 (UTC) reply

If I am not completely mistaken, then the continuity of C at theta only guarantees f* to be continuous at theta and C* to be upper hemicontinuous and compact valued at theta, not globally. 120.51.141.38 ( talk) 05:04, 19 May 2023 (UTC) reply