On continuous noncomplete lattices |
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Authors: | K V Adaricheva V A Gorbunov M V Semenova |
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Institution: | (1) 134 South Lombard ave, Oak Park, lllinois 60302, USA, e-mail: ki13ra@yahoo.com, US;(2) Sobolev's Institute of Mathematics, Siberian Branch of Russian Academy of Science, 4 Prospect of Academician Koptug, 630090 Novosibirsk, Russia, e-mail: semenova@math.nsc.ru, RU |
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Abstract: | We consider noncomplete continuous and algebraic lattices and prove that finitely generated free lattices are algebraic.
We also study the Lawson topology, the second most important topology in the theory of continuous domains, on finitely presented
lattices. In particular, we prove that algebraic finitely presented lattices are linked bicontinuous and the Lawson topology
on these lattices coincides with the interval topology. Several examples of non-distributive and noncomplete algebraic and
continuous lattices are given in the paper.
Received April 5, 2000; accepted in final form December 12, 2000. |
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Keywords: | and phrases: Lattice continuous finitely presented Lawson topology interval topology |
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