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A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
George A. Grätzer (Hungarian: Grätzer György; born 2 August 1936, in Budapest) is a Hungarian-Canadian mathematician, specializing in lattice theory and universal algebra. He is known for his books on LaTeX [1] and his proof with E. Tamás Schmidt of the Grätzer–Schmidt theorem. [2] [3]
A residuated lattice is a lattice. (def) 15. A distributive lattice is modular. [3] 16. A modular complemented lattice is relatively complemented. [4] 17. A boolean algebra is relatively complemented. (1,15,16) 18. A relatively complemented lattice is a lattice. (def) 19. A heyting algebra is distributive. [5] 20. A totally ordered set is a ...
A Hasse diagram of Young's lattice. In mathematics, Young's lattice is a lattice that is formed by all integer partitions.It is named after Alfred Young, who, in a series of papers On quantitative substitutional analysis, developed the representation theory of the symmetric group.
Pages in category "Lattice theorists" The following 18 pages are in this category, out of 18 total. This list may not reflect recent changes. B. Garrett Birkhoff; D.
Introduction to Lattices and Order is a mathematical textbook on order theory by Brian A. Davey and Hilary Priestley.It was published by the Cambridge University Press in their Cambridge Mathematical Textbooks series in 1990, [1] [2] [3] with a second edition in 2002.
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
In pointless topology we take these properties of the lattice as fundamental, without requiring that the lattice elements be sets of points of some underlying space and that the lattice operation be intersection and union. Rather, point-free topology is based on the concept of a "realistic spot" instead of a point without extent.