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Localic Krull dimension
Author(s) -
Bezhanishvili Guram,
Bezhanishvili Nick,
LuceroBryan Joel,
van Mill Jan
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610437
Subject(s) - krull dimension , dimension (graph theory) , mathematics , dimension theory (algebra) , topological space , space (punctuation) , topology (electrical circuits) , global dimension , pure mathematics , discrete mathematics , combinatorics , algebra over a field , computer science , noetherian , operating system
We shall define localic Krull dimension for topological spaces. In particular, a space X has the localic Krull dimension n if n is the greatest number such that X can be mapped, via a continuous and open map, onto the n ‐chain seen as an Alexandroff space. We shall discuss the applications of this concept in obtaining topological completeness results in modal logic. We shall also show how the localic Krull dimension is related to the Krull dimension in ring theory. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)