کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
422810 | 685144 | 2014 | 10 صفحه PDF | دانلود رایگان |
In this paper, concepts of strongly way below relations, completely precontinuous posets, coprimes and Heyting posets are introduced. The main results are: (1) The strongly way below relations of completely precontinuous posets have the interpolation property; (2) A poset P is a completely precontinuous poset iff its normal completion is a completely distributive lattice; (3) An ω-chain complete P is completely precontinuous iff P and Pop are precontinuous and its normal completion is distributive iff P is precontinuous and has enough coprimes; (4) A poset P is completely precontinuous iff the strongly way below relation is the smallest approximating auxiliary relation on P iff P is a Heyting poset and there is a smallest approximating auxiliary relation on P. Finally, given a poset P and an auxiliary relation on P, we characterize those join-dense subsets of P whose strongly way-below relation agrees with the given auxiliary relation.
Journal: Electronic Notes in Theoretical Computer Science - Volume 301, 18 February 2014, Pages 169-178