Continuous Lattices and Domains

By G. Gierz, K. Hofmann, K. Keimel, Jimmie Lawson, M. Mislove, D. Scott. 2003

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$M$-fuzzifying interval spaces (2017, background): “An element a in M is called co-prime if a 6 b∨ c implies a 6 b or a 6 c [5].”
Pullbacks, $C(X)$-algebras, and their Cuntz semigroup (2011, background): “Adopting the terminology of [15], we will say that an object M in Cu is countably based if there is a countable subset X in M such that every element of M is the supremum of a rapidly increasing sequence of elements coming from X.”
Infinite distributive laws versus local connectedness and compactness properties (2009, background): “[25]).”
On T0 spaces determined by well-filtered spaces (2019, methodology): “([8]) For a nonempty family {Ki : i ∈ I} ⊆ K(X), ∨ i∈I Ki exists in K(X) iff ⋂ i∈I Ki ∈ K(X).”
Monoidal topology : a categorical approach to order, metric, and topology (2014, methodology): “Lemma 5.3.4 is part of Exercise II.34 of [Gierz et al., 2003], contributed by Escardó and Heckmann.”
Quivers of monoids with basic algebras (2011, methodology): “We sketch a proof using semilattice duality [37,39,42].”