Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 between the category of Priestley spaces and the category of bounded...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 between the category of Priestley spaces and the category of bounded distributive lattices. A Priestley space is an ordered topological space (X, ,<=), i. e. a set X equipped with a partial order <= and a topology , satisfying the following two conditions: (i) (X, ) is compact. (ii) If scriptstyle x,notle, y, then there exists a clopen up-set U of X such that x U and y U. (This condition is known as the Priestley separation axiom.). Priestley spaces are closely related to spectral spaces. For a Priestley space (X, ,<=), let u denote the collection of all open up-sets of X. Similarly, let d denote the collection of all open down-sets of X.
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