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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)

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