Every Boolean algebra is a Heyting algebra when a → b is defined as usual as ¬ a ∨ b, as is every complete distributive lattice when a → b is taken to be the supremum of the set of all c for which a ∧ c ≤ b. The open sets of a topological space form a complete distributive lattice and hence a Heyting algebra.

* Every Boolean algebra is a distributive lattice.

* Every Heyting algebra is a distributive lattice.

* Every totally ordered set is a distributive lattice with max as join and min as meet.

Every complemented distributive lattice has a unique orthocomplementation and is in fact a Boolean algebra.

Every lattice element of the structure is in its proper place, whether it is a single atom or a molecular grouping.

* Every totally ordered set that is a bounded lattice is also a Heyting algebra, where is equal to when, and 1 otherwise.

Every complete lattice is also a bounded lattice, which is to say that it has a greatest and least element.

Every lattice in can be generated from a basis for the vector space by forming all linear combinations with integer coefficients.

* Every substructure is the union of its finitely generated substructures ; hence Sub ( A ) is an algebraic lattice.

Also, a kind of converse holds: Every algebraic lattice is isomorphic to Sub ( A ) for some algebra A.

Every non-modular lattice contains a copy of N < sub > 5 </ sub > as a sublattice.

Every quasinormal subgroup is a modular subgroup, that is, a modular element in the lattice of subgroups.

Every legislator from Brasstown Bald to Folkston is going to have his every vote subjected to the closest scrutiny as a test of his political allegiances, not his convictions.

Every detail in his interpretation has been beautifully thought out, and of these I would especially cite the delicious laendler touch the pianist brings to the fifth variation ( an obvious indication that he is playing with Viennese musicians ), and the gossamer shading throughout.

Every taxpayer is well aware of the vast size of our annual defense budget and most of our readers also realize that a large portion of these expenditures go for military electronics.

Every single problem touched on thus far is related to good marketing planning.

Every few days, in the early morning, as the work progressed, twenty men would appear to push it ahead and to shift the plank foundation that distributed its weight widely on the Rotunda pavement, supported as it is by ancient brick vaulting.

Every dream, and this is true of a mental image of any type even though it may be readily interpreted into its equivalent of wakeful thought, is a psychic phenomenon for which no explanation is available.

Every man in every one of these houses is a Night Rider.

Every library borrower, or at least those whose taste goes beyond the five-cent fiction rentals, knows what it is to hear the librarian say apologetically, `` I'm sorry, but we don't have that book.

Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Every infinite game in which is a Borel subset of Baire space is determined.

Every natural-born citizen of a foreign state who is also an American citizen and every natural-born American citizen who is a citizen of a foreign land owes a double allegiance, one to the United States, and one to his homeland ( in the event of an immigrant becoming a citizen of the US ), or to his adopted land ( in the event of an emigrant natural born citizen of the US becoming a citizen of another nation ).

Every line of written text is a mere reflection of references from any of a multitude of traditions, or, as Barthes puts it, " the text is a tissue of quotations drawn from the innumerable centres of culture "; it is never original.

Every root of a polynomial equation whose coefficients are algebraic numbers is again algebraic.

* Every rectangle R is in M. If the rectangle has length h and breadth k then a ( R ) =

Every year, on the last Sunday in April, there is an ice fishing competition in the frozen estuarine waters of the Anadyr River's mouth.

Every bounded positive-definite measure μ on G satisfies μ ( 1 ) ≥ 0. improved this criterion by showing that it is sufficient to ask that, for every continuous positive-definite compactly supported function f on G, the function Δ < sup >– ½ </ sup > f has non-negative integral with respect to Haar measure, where Δ denotes the modular function.

Every AP defines a top data models to be used for data exchange, called the Application Integrated Model ( AIM ) or in the case of a modular AP called Module Integrated Models ( MIM ).

Every modular function will have this general kind of self-similarity.

Every modular function will have this general kind of self-similarity.

Every time I closed my eyes, I saw Gray Eyes rushing at me with a knife.

Every movement she made seemed unnecessarily noisy.

`` Every last one of you.

Every plane that could fly was sent into the air.

Every so often the diminishing sound of a car came under the trailer as it slowed down for the wreck then speeded up again as it got clear.

Every so often he turned the knife.

Every bone and muscle in his body showed, but he did not give the appearance of starving.

Every path from back door to barn was covered by a grape-arbor, and every yard had its fruit trees.

Every morning early, in the summer, we searched the trunks of the trees as high as we could reach for the locust shells, carefully detached their hooked claws from the bark where they hung, and stabled them, a weird faery herd, in an angle between the high roots of the tulip tree, where no grass grew in the dense shade.

Every slight sound that rose against that pressure fell away again, crushed beneath it.

They give strict interpretation to William James' statement that `` Every idea that enters the mind tends to express itself ''.

Every morning contingents of prisoners would be sent out to labor in nearby factories.

If nothing else, at least two good songs came out of the project, `` Out Of This World '' and `` June Comes Around Every Year ''.

Every day, when the President took his nap, Rob Roy would stretch out on the window seat near him, like a perfect gentleman, and stare thoughtfully out the window, or he would take a little nap himself.

Every First Family seems to have one couple upon whom it relies for true friendship.

Every letter answers itself in a couple of weeks ''.

Every recorded request by Thomas for a delay in a flank movement or an advance was to gain time to take care of his horses.

Every chance I got I left the hotel to visit Lilly.

Every man who dabbles in the market to make a little easy money on the side and suffers losses could at the time hardly face his wife who was wondering how her husband could be so dumb.

Sir -- Every resident of this city should visit the Newark Museum and see the exhibit `` Our Changing Skyline in Newark ''.

Every soldier in the army has, somewhere, relatives who are close to starvation.

Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.

Every eye was on him as he began to speak.

Every time he moved or said something, the chair creaked again.