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Dimension of Binary Convex Structures
Author(s) -
van de Vel M.
Publication year - 1984
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-48.1.34
Subject(s) - mathematics , convexity , dimension (graph theory) , quotient , pure mathematics , distributive property , binary number , regular polygon , space (punctuation) , product (mathematics) , quotient space (topology) , convex analysis , combinatorics , convex optimization , geometry , arithmetic , computer science , financial economics , economics , operating system
It is shown that for compact spaces with a normal binary convexity, the dimension functions dim, ind, Ind, and cohomological dimension are all equal. Also, an n ‐dimensional compact space X with a normal binary convexity embeds in a product of an n ‐dimensional connected quotient of X with the space of X components. Both results are obtained with the aid of an auxiliary theory of convex dimension. Some applications to completely distributive lattices are given.