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...'' ≠ 0 and ''c'' has no nontrivial common predecessor with ''a''. That is, in the latter case, the only ''x'' with ''x'' ≤ ''a'' and ''x'' ≤ ''c'' is ...of a [[topological space]] could be defined in terms of its [[distributive lattice]] of [[closed set]]s. He observed that the inclusion order on the closed se ...

{{Short description|Law in algebra}} In [[algebra]], the '''absorption law''' or '''absorption identity''' is an [[ ...

{{for|duals of order-theoretic lattices|Duality (order theory) }} {{Group theory sidebar |Discrete}} ...

{{Short description|1990 book on mathematical order theory}} ...of the [[Mathematical Association of America]] has suggested its inclusion in undergraduate mathematics libraries.{{r|maa}} ...

In [[group theory]], the '''correspondence theorem'''<ref name="Robinson2003"> |title=A Course in Group Theory ...

...he [[Riesz space#Projection properties|principal projection property]] can in a sense be approximated uniformly by [[simple function]]s. ...e [[Poisson kernel|Poisson formula]] and the [[spectral theorem]] from the theory of [[normal operator]]s can all be shown to follow as special cases of the ...

...on|Correlation-type inequality for four functions on a finite distributive lattice}} ...r functions on a finite [[distributive lattice]]. It is a fundamental tool in [[statistical mechanics]] and [[Combinatorics#Probabilistic_combinatorics|p ...

...]. The theorem was proved by the Hungarian mathematician [[György Hajós]] in 1941 using [[group ring]]s. [[László Rédei|Rédei]] later proved the sta [[File:Shifted square tiling.svg|thumb|160px|In this lattice tiling of the plane by congruent squares, the green and violet squares meet ...

.... [[Duality (category theory)|Dually]], a '''cocomplete category''' is one in which all small [[colimit]]s exist. A '''bicomplete category''' is a catego ==Theorems== ...

{{short description|Ideals in a Boolean algebra can be extended to prime ideals}} ...[[order theory]]). This article focuses on prime ideal theorems from order theory. ...

...ice is&mdash;up to [[order isomorphism|isomorphism]]&mdash;given as such a lattice of sets. ...rrespondence are discussed in the article on [[lattice (order)|lattices]]. In the present situation, the algebraic description appears to be more conveni ...

{{short description|Result in the mathematics of string theory on a functor that quantizes bosonic strings}} ...athematics]], and in particular in the mathematical background of [[string theory]], the '''Goddard–Thorn theorem''' (also called the '''no-ghost theorem'' ...

...ge = [[File: Goetze friedrich.jpg|frameless|{{center|Friedrich Götze in 2010}}]] ...izing in [[probability theory]], [[mathematical statistics]], and [[number theory]]. ...

...h ''F''(''x'') = ''x''), under some conditions on ''F'' that can be stated in general terms.<ref>{{cite book | title = Fixed Point Theory and Its Applications ...

...omenon can be reformulated entirely in terms of gauge invariant quantities in what is known as the Fröhlich–Morchio–Strocchi mechanism.<ref>{{cite j ==Theory== ...

{{Short description|Group of mathematical theorems}} ...other [[algebraic structure]]s. In [[universal algebra]], the isomorphism theorems can be generalized to the context of algebras and [[congruence relation|con ...

.../bfm%3A978-3-540-38933-0%2F1.pdf|chapter=Front matter|series=Lecture Notes in Computer Science |isbn=3-540-13378-X |s2cid=7488558 }}</ref> ...point <math>\mu (x, y).(f, g)(x, y)</math>, a pair <math>(x_0, y_0)</math> in <math>P \times Q</math> such that <math>f (x_0, y_0) = x_0</math> and <math ...

:''This is about [[lattice theory]]. For other similarly named results, see [[Birkhoff's theorem (disambiguat ...s way. It is named after [[Garrett Birkhoff]], who published a proof of it in 1937.<ref name="birkhoff">{{harvtxt|Birkhoff|1937}}.</ref> ...

...to color some of the white points black so that the number of black points in the rows and columns match the blue numbers.]]'''Discrete tomography'''<ref Herman, G. T. and Kuba, A., Advances in Discrete Tomography and Its Applications, Birkhäuser Boston, 2007 ...

...eals are of great importance for many constructions in order and [[lattice theory]]. ...{mvar|I}} and ''y'' in ''P'', {{math|''y'' ≤ ''x''}} implies that ''y'' is in {{mvar|I}} &nbsp;({{mvar|I}} is a [[lower set]]), ...