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A generalization of boundedly compact metric spaces

Gerald Beer, Anna Di Concilio (1991)

Commentationes Mathematicae Universitatis Carolinae

A metric space X , d is called a UC space provided each continuous function on X into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that UC spaces play relative to the compact metric spaces.

Baire-one mappings contained in a usco map

Ondřej F. K. Kalenda (2007)

Commentationes Mathematicae Universitatis Carolinae

We investigate Baire-one functions whose graph is contained in the graph of a usco mapping. We prove in particular that such a function defined on a metric space with values in d is the pointwise limit of a sequence of continuous functions with graphs contained in the graph of a common usco map.

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