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Every and countable
* Countably compact: Every countable open cover has a finite subcover.
Every subset of the Hilbert cube inherits from the Hilbert cube the properties of being both metrizable ( and therefore T4 ) and second countable.
It is more interesting that the converse also holds: Every second countable T4 space is homeomorphic to a subset of the Hilbert cube.
* Every totally disconnected compact metric space is homeomorphic to a subset of a countable product of discrete spaces.
For example, second-order arithmetic can express the principle " Every countable vector space has a basis " but it cannot express the principle " Every vector space has a basis ".
: Every countable theory which is satisfiable in a model is also satisfiable in a countable model.
* Every first countable space is sequential.
* Every compact space is σ-compact, and every σ-compact space is Lindelöf ( i. e. every open cover has a countable subcover ).
:# Every element of D is the least upper bound of a countable increasing sequence of isolated elements.
* Every collection of disjoint open sets in a second-countable space is countable.

Every and theory
* Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by " reversing all the arrows ".
Every well-constructed theory of education has at its center a philosophical anthropology.
Every field theory of particle physics is based on certain symmetries of nature whose existence is deduced from observations.
While also refining Galen's erroneous theory of the pulse, Avicenna provided the first correct explanation of pulsation: " Every beat of the pulse comprises two movements and two pauses.
Every epimorphism in this algebraic sense is an epimorphism in the sense of category theory, but the converse is not true in all categories.
Every one of the features encompassed by the theory still requires a reason for it to be maintained after hominids left the aquatic environment.
" Some also hold to the theory that Kidd conspired with Henry Every and Oak Island was used as a pseudo community bank between the two.
# Every " good " scientific theory is a prohibition: it forbids certain things to happen.
# Every genuine test of a theory is an attempt to falsify it, or to refute it.
Every vector bundle theory ( real, complex etc.
Iwasawa worked with so-called-extensions: infinite extensions of a number field with Galois group isomorphic to the additive group of p-adic integers for some prime p. Every closed subgroup of is of the form, so by Galois theory, a-extension is the same thing as a tower of fields such that.
Every computer must be compatible with the principles of information theory, statistical thermodynamics, and quantum mechanics.
Is fundamental for the many-body theory that Every operator can be expressed in terms of annihilation and creation operators.
Every Skolem theory is model complete, i. e. every substructure of a model is an elementary substructure.
Every issue of the magazine opens with a description of The Skeptics Society and its mission statement, which is to explore subjects such as creationism, pyramid power, Bigfoot, pseudohistorical claims ( as in the examples of Holocaust denial and extreme Afrocentrism ), the use or misuse of theory and statistics, conspiracy theories, urban myths, witch-hunts, mass hysterias, genius and intelligence, and cultural influences on science, as well as controversies involving protosciences at the leading edge of established science, and even fads like cryonics and low-carb diets.
Every proper subgroup of G can be assumed a solvable group, meaning that much theory of such subgroups could be applied.
Every quantum field theory satisfying certain technical assumptions about its S-matrix that has non-trivial interactions can only have a symmetry Lie algebra which is always a direct product of the Poincaré group and an internal group if there is a mass gap: no mixing between these two is possible.
Every major Korean neo-Confucianist shared Toegye's preoccupation with single-mindedness, which signalled new stress on praxis in the development of Korean neo-Confucianism: the fusion of the metaphysical and the physical is better brought about through action than speculation, important as theory might be.
# Every elementary substructure of a model of a theory T also satisfies T ; hence it is a submodel.
Every theory with quantifier elimination is model complete.
Every theory which refuses to ascribe to God an attribute which is essential to a worthy conception of His character is anti-theistic.

Every and which
Every new scandal which would provide more `` copy '' for Marshall's pen would thus mean more publicity for Welch.
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 family of Riviera Presbyterian Church has been asked to read the Bible and pray together daily during National Christian Family Week and to undertake one project in which all members of the family participate.
** Zorn's lemma: Every non-empty partially ordered set in which every chain ( i. e. totally ordered subset ) has an upper bound contains at least one maximal element.
* Every continuous functor on a small-complete category which satisfies the appropriate solution set condition has a left-adjoint ( the Freyd adjoint functor theorem ).
** Every infinite game in which is a Borel subset of Baire space is determined.
Every telephone company, whether large or small, determines its own ANAC for each individual central office, which tends to perpetuate the current situation of a mess of overlapping and / or spotty areas of coverage.
: Every non-empty set A contains an element B which is disjoint from A.
Every field has an algebraic extension which is algebraically closed ( called its algebraic closure ), but proving this in general requires some form of the axiom of choice.
Every year since 1972 the BVI has hosted the Spring Regatta, which is a seven-day collection of sailing races throughout the islands.
* Every real Banach algebra which is a division algebra is isomorphic to the reals, the complexes, or the quaternions.
* Every unital real Banach algebra with no zero divisors, and in which every principal ideal is closed, is isomorphic to the reals, the complexes, or the quaternions.
Every character is automatically continuous from A to C, since the kernel of a character is a maximal ideal, which is closed.
Every computer contains an internal clock that regulates the rate at which instructions are executed and synchronizes all the various computer components.
Every context-sensitive grammar which does not generate the empty string can be transformed into an equivalent one in Kuroda normal form.
According to Every, one example may be " the myth of St. George " and other stories about saints battling dragons, which were " modelled no doubt in many cases on older representations of the creator and preserver of the world in combat with chaos ".
Every argues that " the disparagement of myth in our own civilization " stems partly from objections to perceived idolatry, objections which intensified in the Reformation, both among Protestants and among Catholics reacting against the classical mythology revived during the Renaissance.
Every grammar in Chomsky normal form is context-free, and conversely, every context-free grammar can be transformed into an equivalent one which is in Chomsky normal form.
Every four years, during which an extra 24 hours have accumulated, one extra day is added to keep the count coordinated with the sun's apparent position.
Every node has a location, which is a number between 0 and 1.
Every sequence can, thus, be read in three reading frames, each of which will produce a different amino acid sequence ( in the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).
Every time the boy had an injury which caused him internal or external bleeding, the Tsarina called on Rasputin, and the Tsarevich subsequently got better.
Every week before June 19, the strip focuses on Garfield's birthday, which he dreads because of his fear of getting older.
::: Every Bill which shall have passed the House of Representatives and the Senate, shall, before it become a Law, be presented to the President of the United States ; If he approves he shall sign it, but if not he shall return it, with his Objections to that House in which it shall have originated ...

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