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On quasi-uniform space valued semi-continuous functions

Tomasz Kubiak, María Angeles de Prada Vicente (2009)

Commentationes Mathematicae Universitatis Carolinae

F. van Gool [Comment. Math. Univ. Carolin. 33 (1992), 505–523] has introduced the concept of lower semicontinuity for functions with values in a quasi-uniform space ( R , 𝒰 ) . This note provides a purely topological view at the basic ideas of van Gool. The lower semicontinuity of van Gool appears to be just the continuity with respect to the topology T ( 𝒰 ) generated by the quasi-uniformity 𝒰 , so that many of his preparatory results become consequences of standard topological facts. In particular, when the order...

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