Displaying similar documents to “Partial dcpo’s and some applications”

Definition of Flat Poset and Existence Theorems for Recursive Call

Kazuhisa Ishida, Yasunari Shidama, Adam Grabowski (2014)

Formalized Mathematics

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This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge....

Tail and free poset algebras.

Mohamed Bekkali, Driss Zhani (2004)

Revista Matemática Complutense

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We characterize free poset algebras F(P) over partially ordered sets and show that they can be represented by upper semi-lattice algebras. Hence, the uniqueness, in decomposition into normal form, using symmetric difference, of non-zero elements of F(P) is established. Moreover, a characterization of upper semi-lattice algebras that are isomorphic to free poset algebras is given in terms of a selected set of generators of B(T).

Topological Interpretation of Rough Sets

Adam Grabowski (2014)

Formalized Mathematics

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Rough sets, developed by Pawlak, are an important model of incomplete or partially known information. In this article, which is essentially a continuation of [11], we characterize rough sets in terms of topological closure and interior, as the approximations have the properties of the Kuratowski operators. We decided to merge topological spaces with tolerance approximation spaces. As a testbed for our developed approach, we restated the results of Isomichi [13] (formalized in Mizar in...

Localic Katětov-Tong insertion theorem and localic Tietze extension theorem

Yong Min Li, Wang Guo-jun (1997)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, localic upper, respectively lower continuous chains over a locale are defined. A localic Katětov-Tong insertion theorem is given and proved in terms of a localic upper and lower continuous chain. Finally, the localic Urysohn lemma and the localic Tietze extension theorem are shown as applications of the localic insertion theorem.

Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras

Jan Paseka, Zdena Riečanová, Junde Wu (2010)

Kybernetika

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We prove that the interval topology of an Archimedean atomic lattice effect algebra E is Hausdorff whenever the set of all atoms of E is almost orthogonal. In such a case E is order continuous. If moreover E is complete then order convergence of nets of elements of E is topological and hence it coincides with convergence in the order topology and this topology is compact Hausdorff compatible with a uniformity induced by a separating function family on E corresponding to compact and cocompact...

Separation properties in congruence lattices of lattices

Miroslav Ploščica (2000)

Colloquium Mathematicae

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We investigate the congruence lattices of lattices in the varieties ℳ n . Our approach is to represent congruences by open sets of suitable topological spaces. We introduce some special separation properties and show that for different n the lattices in ℳ n have different congruence lattices.

More on the Continuity of Real Functions

Keiko Narita, Artur Kornilowicz, Yasunari Shidama (2011)

Formalized Mathematics

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In this article we demonstrate basic properties of the continuous functions from R to Rn which correspond to state space equations in control engineering.