Separately continuous algebras
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 \textit{E. Nelson}, Lect. Notes Math. 871, 315-334 (1981; Zbl 0493.08008)].
free separately \(\Delta\)-continuous algebras
scientific article; zbMATH DE number 3847460