The algebra of implicit operations |
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Authors: | Jorge Almeida |
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Institution: | (1) Centro de Matemática Faculdade de Ciências, Universidade do Porto, Porto, Portugal |
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Abstract: | For an ordinal and a class
of topological algebras of a given type (which may be infinite and may contain inflnitary operations), an -aryimplicit operation on
is any new![rdquo](/content/v041x78v8m552524/xxlarge8221.gif) -ary operation whose introduction does not eliminate any continuous homomorphisms between members of
. The set of all -ary implicit operations on
is denoted by
and forms an algebra of the given type which is endowed with the least topology making continuous all homomorphisms into members of
. With this topology,
is a topological algebra in which the subalgebra
of all -ary operations on
which are induced by terms is dense, provided that
is closed under the formation of closed subalgebras and finitary direct products. This is obtained by realizing
as an inverse limit of -generated members of
. These results are applied to pseudovarieties of topological and finite algebras.This work was supported, in part, by INIC grant 85/CEX/4. This paper was written while the author was a faculty member at the Universidade do Minho.Presented by Ralph McKenzie. |
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Keywords: | |
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