File:Birkhoff representation theorem.gif
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Summary
| Description | Example of Birkhoff's representation theorem for distributive lattices. The join-irreducible elements (nodes) of the distributive example lattice are shadowed, and named a,...,g for reference purposes. They satisfy the relations f < d < a, f < c < a, g < e < b, g < c < b. By Birkhoff's theorem, the set of all down-sets built of these elements, ordered by set inclusion, is isomorphic to the original lattice. For each node, the down-set it corresponds to is shown in blue, with set braces {} omitted for brevity. | ||
| Date | |||
| Source | Own work, inspired by Fig.8.3 (p.167) of B.A. Davey and H.A. Priestley (1990) Introduction to Lattices and Order, Cambridge Mathematical Textbooks, Cambridge University Press | ||
| Author | Jochen Burghardt | ||
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 21:13, 29 January 2016 | | 423 × 723 (7 KB) | wikimediacommons>Jochen Burghardt | tried to improve readability: boldface for shadowed nodes, darker colors |
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