Abstract: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 Mero\~no 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.
Keywords: realcompactness; realcompleteness; uniform space
DOI: DOI 10.14712/1213-7243.2015.225
AMS Subject Classification: 54E15 54D60