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Separately continuous algebras. (English) Zbl 0534.08006

An ordered algebra is separately \(\Delta\)-continuous if it has directed joins, and the operations preserve these joins in each variable separately. For infinitary signatures, free separately \(\Delta\)- continuous algebras are proved not to exist, in contrast with the jointly continuous algebras [see E. Nelson, Lect. Notes Math. 871, 315-334 (1981; Zbl 0493.08008)].

MSC:

08B20 Free algebras
06F99 Ordered structures

Citations:

Zbl 0493.08008
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References:

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