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Une méthode générale de compactification d’un ensemble, et applications aux opérateurs induits par des transformations ponctuelles continues. (A general method of compactification of a set and applications to operators induced by continuous point transformations). (French) Zbl 0736.54019
Relations between compactifications and systems of real-valued or complex-valued functions are investigated. Results in the first part are known. In the last part a semigroup structure on \(X\) is extended to a semigroup structure on a compactification of \(X\), and applications of inverting functions to series are given (for some \(\{a_ k\}\) there exists \(\{b_ k\}\) or \(\{c_ k\}\) with \((\sum a_ k e^{ikqx})^{- 1}=\sum b_ k e^{ikqx}\), or (\(\sum^ n_{k=1}a_ k)^{-1}=\sum^ n_{k=1}c_ k\) for each \(n\)).
Reviewer: M.Hušek (Praha)

54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54C40 Algebraic properties of function spaces in general topology
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