A compactification of the algebra of terms. (English) Zbl 0358.08001

Let \(Q_\sigma\) be the absolutely free algebra of terms of a given similarity type \(\sigma\). As a natural completion of \(Q_\sigma\) the algebra \(R_\sigma\) of generalized infinite terms is constructed. The main result is:
Theorem 3. There exists a compact Hausdorff topology on \(R_\sigma\) in which all the operations of \(Q_\sigma\) (and \(R_\sigma\) of course) are continuous.
Corollary 4 states that \(R_\sigma\) is equationally compact.
The paper is concluded by some related problems.


08B20 Free algebras
08A45 Equational compactness
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
Full Text: DOI


[1] B. Banaschewski,On equationally compact extensions of algebras, Algebra Universalis,4 (1974), 20–35. · Zbl 0314.08005 · doi:10.1007/BF02485702
[2] W. Taylor,Some constructions of compact algebras, Annals of Math. Logic,3 (1971), 395–435. · Zbl 0239.08003 · doi:10.1016/0003-4843(71)90012-X
[3] W. Taylor,Residually small varieties, Algebra Universalis,2 (1972), 33–53. · Zbl 0263.08005 · doi:10.1007/BF02945005
[4] B. Węglorz,Equationally compact algebras (I), Fund. Math.59 (1966), 289–298.
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