Abstract
In the first section of the article a basic construction to be used later is described, and some of its properties are studied. In the second section a basic property of mappings obtained with the help of the basic construction is defined and a number of results about the compactification of mappings with this property are proved; moreover, the construction is here applied to construct compactifications satisfying the first axiom of countability and absolutes. The third section is devoted to a survey of the basic results in the theory of compactifications satisfying the first axiom of countability. In the fourth section are given examples of Cech-complete separable Lindelof spaces satisfying the first axiom of countability, which do not have compactifications of countable tightness.Figures: 1. Bibliography: 19 titles.
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