Lower Semi-continuous Function Frames |
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Authors: | Christophe Van Olmen Stijn Verwulgen |
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Affiliation: | 1. Dept. Wiskunde-informatica, Universiteit Antwerpen, Middelheimlaan 1, 2020, Antwerpen, Belgium
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Abstract: | It has never been systematically studied under which algebraic actions lower semi-continuity is a stable property. This is despite the fact that this continuity variant is commonly used, in different branches of mathematics. In this note we propose an abstraction of the lower semi-continuous function frame on a topological space and describe this as the Eilenberg–Moore algebras of a Hom-functor monad. We also point out the connection with approach frames and with classical frame theory. Thereby we obtain several different characterizations of the introduced category. |
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