In 1960, José Morgado gave a necessary and sufficient condition on a poset P in order that closure operators on P, ordered pointwise, form a complete lattice. This result was based on a notion of relative quasi-infimum in posets. This note shows that Morgado's result is flawed.
A counterexample to a result concerning closure operators
RANZATO, FRANCESCO
2001
Abstract
In 1960, José Morgado gave a necessary and sufficient condition on a poset P in order that closure operators on P, ordered pointwise, form a complete lattice. This result was based on a notion of relative quasi-infimum in posets. This note shows that Morgado's result is flawed.
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