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Definition of Upper semi-continuous
1. Adjective. (context: of a real-valued function on a topological space) Such that, for each fixed number, the subspace of points whose images are at least that number is closed. ¹
2. Adjective. (context: of a real-valued function on a topological space) Such that for each fixed point ''x'' there is some neighborhood whose image's limit superior is ''x''
¹ Source: wiktionary.com
Lexicographical Neighbors of Upper Semi-continuous
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