Transporting continuity properties from a poset to its subposets

DOI10.1016/J.TCS.2022.02.021arXiv1301.0999MaRDI QIDQ6238531

Publication date: 6 January 2013

Abstract: We identify two key conditions that a subset

A

of a poset

P

may satisfy to guarantee the transfer of continuity properties from

P

to

A

. We then highlight practical cases where these key conditions are fulfilled. Along the way we are led to consider subsets of a given poset

P

whose way-below relation is the restriction of the way-below relation of

P

, which we call way-below preserving subposets. As an application, we show that every conditionally complete poset with the interpolation property contains a largest continuous way-below preserving subposet. Most of our results are expressed in the general setting of Z theory, where Z is a subset system.

Mathematics Subject Classification ID

Continuous lattices and posets, applications (06B35)

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