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Intrinsic Spectral Topologies
Author(s) -
PRIESTLEY H. A.
Publication year - 1994
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1994.tb44135.x
Subject(s) - partially ordered set , topology (electrical circuits) , network topology , prime (order theory) , distributive property , mathematics , commutative property , comparison of topologies , order (exchange) , pure mathematics , combinatorics , general topology , computer science , extension topology , topological space , operating system , finance , economics
Given a poset ( X ; ≤), any spectral topology with specialisation order ≤ lies between the upper topology and the Scott topology. Conditions are given under which these extreme topologies are indeed spectral. The results contribute to the understanding of speectral sets , that is, posets which arise as the prime ideals of commutative rings with 1, ordered by inclusion, or equivalently as the prime ideals of distributive lattices with 0 and 1, ordered by inclusion.