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On completions of pseudo-normed BCK-algebras and pseudo-metric universal algebras. (English) Zbl 0666.08005

It is shown that if a class C of pseudo-metric algebras is closed under subalgebras, homomorphic images and countable direct powers, then the metric identification and the metric completion of any algebra from C belongs to C, too.
It is also shown that the closedness under homomorphic images is no necessary condition - a class of BCK-algebras is the example given to show this.
Reviewer: M.Pałasiński

MSC:

08B99 Varieties
54H99 Connections of general topology with other structures, applications
06F99 Ordered structures
54E25 Semimetric spaces
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