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Variations of uniform completeness related to realcompactness

Miroslav Hušek — 2017

Commentationes Mathematicae Universitatis Carolinae

Various characterizations of realcompactness are transferred to uniform spaces giving non-equivalent concepts. Their properties, relations and characterizations are described in this paper. A Shirota-like characterization of certain uniform realcompactness proved by Garrido and Meroño for metrizable spaces is generalized to uniform spaces. The paper may be considered as a unifying survey of known results with some new results added.

Mazur-like topological linear spaces and their products

Miroslav Hušek — 1997

Commentationes Mathematicae Universitatis Carolinae

Topological linear spaces having the property that some sequentially continuous linear maps on them are continuous, are investigated. It is shown that such properties (and close ones, e.g., bornological-like properties) are closed under large products.

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