Priestly properties
In mathematics, a Priestley space is an ordered topological space with special properties. Priestley spaces are named after Hilary Priestley who introduced and investigated them. Priestley spaces play a fundamental role in the study of distributive lattices. In particular, there is a duality ("Priestley … See more A Priestley space is an ordered topological space (X,τ,≤), i.e. a set X equipped with a partial order ≤ and a topology τ, satisfying the following two conditions: 1. (X,τ) is compact. 2. If See more Priestley spaces are closely related to spectral spaces. For a Priestley space (X,τ,≤), let τ denote the collection of all open up-sets of X. Similarly, let τ denote the collection of all … See more • Spectral space • Pairwise Stone space • Distributive lattice See more • Each Priestley space is Hausdorff. Indeed, given two points x,y of a Priestley space (X,τ,≤), if x≠ y, then as ≤ is a partial order, either $${\displaystyle \scriptstyle x\,\not \leq \,y}$$ or $${\displaystyle \scriptstyle y\,\not \leq \,x}$$. Assuming, without loss of generality, that See more Priestley spaces are also closely related to bitopological spaces. Theorem: If (X,τ,≤) is a Priestley space, then (X,τ ,τ ) is a See more WebProperty details for Priestley Way. One of many properties to rent in Cambuslang Investment Park, Cambuslang, G32 8NB from Savills, world leading estate agents.
Priestly properties
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