Every Hilbert space X is a Banach space because, by definition, a Hilbert space is complete with respect to the norm associated with its inner product, where a norm and an inner product are said to be associated if for all x ∈ X.

# Every infinite subset of X has a complete accumulation point.

Every compact metric space is complete, though complete spaces need not be compact.

Every soul has to follow the path, as explained by the Jinas and revived by the tirthankaras, to attain complete liberation or nirvana.

*( BCT1 ) Every complete metric space is a Baire space.

Every time Emperor Wen sent generals out on battles, he required them to follow the complete battle plans that he had drafted, and even the dates for battles needed approval from the emperor.

Every use of a bank machine, payment by credit card, use of a phone card, call from home, checked out library book, rented video, or otherwise complete recorded transaction generates an electronic record.

Every logical calculation, from the simplest to the most complex, must complete in one clock cycle.

Every time he is thrown out of the house, he is shown wearing the same shirt although he does not always wear it when he is thrown out ( the producers never shot a second sequence with Jazz being thrown out of the house, only adjusting the original scene for time purposes ; an exception is in the episode " Community Action ", where Jazz was thrown out along with a lifesize cardboard cut-out of Bill Cosby, complete with a blooper showing Jeff Townes reshooting his flying off the house several times ).

Every two years, before migration, the adult Common Crane undergoes a complete moult, remaining flightless for six weeks, until the new feathers grow.

*( BCT1 ) Every complete metric space is a Baire space.

Every complete musical piece projects a single key and ultimately a single stufe ( the tonic ).

Every student who intents to pass the matura is required to complete four exams:

Every projective variety is complete, but not vice versa.

" Every opening phase of a Canadian operation was a complete success and the staff works a mathematical masterpiece … the Canadian Army never followed up their opening successes to reach a complete victory.

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 5 years, each Commission conducts a complete review of all constituencies in its part of the United Kingdom.

Every month, a employer must file a complete IR348 Employer monthly schedule with the IRD, stating the income and deductions of each employee.

Every Skolem theory is model complete, i. e. every substructure of a model is an elementary substructure.

Every bounded linear transformation from a normed vector space to a complete, normed vector space can be uniquely extended to a bounded linear transformation from the completion of to.

Every year on the third Saturday in September, German-Americans celebrate the Annual Steuben Parade on Fifth Avenue and an Oktoberfest-style beer fest complete with food and live music in Central Park.

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

Every distributive lattice is modular.

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.