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The natural methods of uniform topology for construction of Wallman compactifications and Wallman realcompactifications are developed. Results on partial order and relations of dimensions in the lattice of compactifications are presented. The construction of the maximal compactification among compactifications of X with fixed realcompactification is given. -
MSC 54E15; 54D35; 54D60; 54F45 . -
Keywords: Uniformity; (Wallman, β-like) compactification; (Wallman) realcompactification; Normal base; Dimension
The various types of ultrafilter-completeness on zero-sets of uniformly continuous functions are introduced, their properties are studied and characterizations in the category are given.
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.
For a uniform space uX the concept of C-u-embedding (C-u*-embedding) in some uniform space is introduced. An analogue of Urysohn's Theorem is proved and it is established, that uX is C-u*-embedded in the Wallman beta-like compactification beta X-u, and any compactification of uX in which uX is C-u*-embedded, must be beta X-u. A uniformly realcompact space is determined. It is proved, that uX is C-u-embedded in the Wallman realcompactification v(u)X, and any uniform realcompactification in which uX is C-u -embedded, is v(u)X.
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
For a Tychonoff space X, the Dieudonne tau-completion of X, denoted by mu TX, is investigated. The space mu TX is defined as the completion of X with respect to the uniformity uTX, where uTX is generated by all continuous mappings of X to metric spaces of weight