Epis need not be dense

In [6] and [7] Meseguer conjectured that in the category Pos(ω) of ω-complete posets and ω-continuous maps the epis are exactly the dense maps. This paper exhibits a counter-example to Meseguer's conjecutre, draws a number of negative conclusions and strengthens another of Meseguer's results. By embedding Pos(ω) in the category of partial algebras of an adequate type, a better understanding is obtained both of these results and of the conjecture.