Abstract
We study isotone self-maps of complete lattices and their fixed point sets, which are complete lattices contained as suborders, but not necessarily as subsemilattices. We develop a representation of such maps by means of relations and show how to navigate their fixed point lattices using a modification of the standard Next closure algorithm. Our approach is inspired by early work of Shmuely [8] and Crapo [1]. We improve and substantially extend our earlier publication [4].
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Ganter, B. Order-Preserving Self-Maps of Complete Lattices. Order 40, 455–468 (2023). https://doi.org/10.1007/s11083-022-09606-6
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DOI: https://doi.org/10.1007/s11083-022-09606-6