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A note on neutral elements in posets

✍ Scribed by B. N. Waphare; Vinayak Joshi

Book ID: 111493032
Publisher: SP Versita
Year: 2009
Tongue: English
Weight: 379 KB
Volume: 59
Category: Article
ISSN: 0139-9918
DOI: 10.2478/s12175-009-0136-1

No coin nor oath required. For personal study only.

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For any poset P let J(P) denote the complete lattice of order ideals in P. J(P) is a contravariant functor in P. Any order-reversing map f: P-+Q can be regarded as an isotone (= order-preserving) map of either P\* into Q or P into Q\*. The induced map of J(Q) to J(P\*) (resp. J(Q\*) into J(P)) will