Hypercontinuous posets

Abstract

The concepts of hypercontinuous posets and generalized completely continuous posets are introduced. It is proved that for a poset P the following three conditions are equivalent: (1) P is hypercontinuous; (2) the dual of P is generalized completely continuous; (3) the normal completion of P is a hypercontinuous lattice. In addition, the relational representation and the intrinsic characterization of hypercontinuous posets are obtained.

Keywords

Hypercontinuous posets / Generalized completely continuous posets / Normal completion

References

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