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Some properties of residuated lattices

Radim Bělohlávek (2003)

Czechoslovak Mathematical Journal

We investigate some (universal algebraic) properties of residuated lattices—algebras which play the role of structures of truth values of various systems of fuzzy logic.

Some Properties of the Sorgenfrey Line and the Sorgenfrey Plane

Adam St. Arnaud, Piotr Rudnicki (2013)

Formalized Mathematics

We first provide a modified version of the proof in [3] that the Sorgenfrey line is T1. Here, we prove that it is in fact T2, a stronger result. Next, we prove that all subspaces of ℝ1 (that is the real line with the usual topology) are Lindel¨of. We utilize this result in the proof that the Sorgenfrey line is Lindel¨of, which is based on the proof found in [8]. Next, we construct the Sorgenfrey plane, as the product topology of the Sorgenfrey line and itself. We prove that the Sorgenfrey plane...

Some Remarkable Identities Involving Numbers

Rafał Ziobro (2014)

Formalized Mathematics

The article focuses on simple identities found for binomials, their divisibility, and basic inequalities. A general formula allowing factorization of the sum of like powers is introduced and used to prove elementary theorems for natural numbers. Formulas for short multiplication are sometimes referred in English or French as remarkable identities. The same formulas could be found in works concerning polynomial factorization, where there exists no single term for various identities. Their usability...

Some remarks on distributive semilattices

Sergio A. Celani, Ismael Calomino (2013)

Commentationes Mathematicae Universitatis Carolinae

In this paper we shall give a survey of the most important characterizations of the notion of distributivity in semilattices with greatest element and we will present some new ones through annihilators and relative maximal filters. We shall also simplify the topological representation for distributive semilattices given in Celani S.A., Topological representation of distributive semilattices, Sci. Math. Japonicae online 8 (2003), 41–51, and show that the meet-relations are closed under composition....

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