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Uniformities for Wallman compactifications and realcompactifications

Asılbek ÇEKEEV

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

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Ultrafilter-completeness on zero-sets of uniformly continuous functions

Asılbek ÇEKEEV

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.

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R-Compact Uniform Spaces in the Category ZUnif

Asılbek ÇEKEEV

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.

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