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51.
We introduce and investigate topo-canonical completions of closure algebras and Heyting algebras. We develop a duality theory
that is an alternative to Esakia’s duality, describe duals of topo-canonical completions in terms of the Salbany and Banaschewski
compactifications, and characterize topo-canonical varieties of closure algebras and Heyting algebras. Consequently, we show
that ideal completions preserve no identities of Heyting algebras. We also characterize definable classes of topological spaces.
Received January 20, 2006; accepted in final form September 12, 2006. 相似文献
52.
Order-compactifications of totally ordered spaces were described by Blatter (J Approx Theory 13:56–65, 1975) and by Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Their results generalize a similar characterization of order-compactifications of linearly ordered spaces, obtained independently
by Fedorčuk (Soviet Math Dokl 7:1011–1014, 1966; Sib Math J 10:124–132, 1969) and Kaufman (Colloq Math 17:35–39, 1967). In this note we give a simple characterization of the topology of a totally ordered space, as well as give a new simplified
proof of the main results of Blatter (J Approx Theory 13:56–65, 1975) and Kent and Richmond (J Math Math Sci 11(4):683–694, 1988). Our main tool will be an order-topological modification of the Dedekind-MacNeille completion. In addition, for a zero-dimensional
totally ordered space X, we determine which order-compactifications of X are Priestley order-compactifications. 相似文献
53.
Guram AS King AO Allen JG Wang X Schenkel LB Chan J Bunel EE Faul MM Larsen RD Martinelli MJ Reider PJ 《Organic letters》2006,8(9):1787-1789
[reaction: see text] New air-stable PdCl(2){P(t)Bu(2)(p-R-Ph)}(2) (R = H, NMe(2), CF(3),) complexes represent simple, general, and efficient catalysts for the Suzuki-Miyaura cross-coupling reactions of aryl halides including five-membered heteroaryl halides and heteroatom-substituted six-membered heteroaryl chlorides with a diverse range of arylboronic acids. High product yields (89-99% isolated yields) and turn-over-numbers (10,000 TON) are observed. 相似文献
54.
Let ${\beta(\mathbb{N})}$ denote the Stone–?ech compactification of the set ${\mathbb{N}}$ of natural numbers (with the discrete topology), and let ${\mathbb{N}^\ast}$ denote the remainder ${\beta(\mathbb{N})-\mathbb{N}}$ . We show that, interpreting modal diamond as the closure in a topological space, the modal logic of ${\mathbb{N}^\ast}$ is S4 and that the modal logic of ${\beta(\mathbb{N})}$ is S4.1.2. 相似文献
55.
We show that subspaces of the space ${\mathbb{Q}}$ of rational numbers give rise to uncountably many d-logics over K4 without the finite model property. 相似文献