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A characterization of inductive posets

In this paper some aspects of the fixedpoint theory of posets are studied. A new type of selfmapping on posets so called ascending mappings is defined. This new concept enables to prove a fixedpoint theorem which is a generalization of the Bourbaki's fixedpoint theorem. This result is applied to two characterizations of inductiveness for posets. The first one shows that inductiveness in semilattices is equivalent to the existence of fixedpoints of extensive mappings The second characterization proves the inductiveness property for general posets.|