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A number of basic properties of R-compact spaces in the category Tych of Tychonoff spaces and their continuous mappings are extended to the category ZUnif of uniform spaces with the special normal bases and their coz-mappings.
In this paper, it is established a characterization of T-normal coverings by means of approximation of the Cech complete paracompacta, which are the perfect preimages of complete metric spaces of weight