Is there an example of a lattice (or just a poset) for which both atoms and co-atoms are useful?
2026-04-08 02:08:49.1775614129
Both atoms and co-atoms in a lattice
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See: A. K. Steiner. On the lattice of topologies. In: Josef Novák (ed.): General Topology and its Relations to Modern Analysis and Algebra. He discusses the lattice of all topologies and (1) states that every topology on X is the supremum of the atoms, but that (2) the co-atoms also generate the lattice and have certain interesting properties which he discusses.