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Page "Descriptive set theory" ¶ 5
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Every and Polish
Every Polish town was bounded to put up a quantity of soldiers-this was a conspicuous sign of a power of a given town how much soldiers it had to put up.
* Every Polish space is homeomorphic to a G < sub > δ </ sub > subspace of the Hilbert cube, and every G < sub > δ </ sub > subspace of the Hilbert cube is Polish.
* Every Polish space is Lusin.
Every Sunday, Polish Radio Katowice broadcasts a program based on famous prewar Lwów's Merry Wave, every Tuesday, Polish Radio Rzeszów broadcasts a program Kresy Landscapes.
Every Polish football club got a ' sponsor ', such as the army, militia or mining industry.
Every prisoner who managed to escape can count on help the moment he reaches the wall of a first Polish farmstead.

Every and space
** Every vector space has a basis.
** Every infinite game in which is a Borel subset of Baire space is determined.
** Every Tychonoff space has a Stone – Čech compactification.
* Theorem Every reflexive normed space is a Banach space.
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 topological space X is a dense subspace of a compact space having at most one point more than X, by the Alexandroff one-point compactification.
* Every compact metric space is separable.
* Every continuous map from a compact space to a Hausdorff space is closed and proper ( i. e., the pre-image of a compact set is compact.
* Pseudocompact: Every real-valued continuous function on the space is bounded.
Every subset A of the vector space is contained within a smallest convex set ( called the convex hull of A ), namely the intersection of all convex sets containing A.
Every compact metric space is complete, though complete spaces need not be compact.
Every point in three-dimensional Euclidean space is determined by three coordinates.
Every node on the Freenet network contributes storage space to hold files, and bandwidth that it uses to route requests from its peers.
Every space filling curve hits some points multiple times, and does not have a continuous inverse.
* Every Lie group is parallelizable, and hence an orientable manifold ( there is a bundle isomorphism between its tangent bundle and the product of itself with the tangent space at the identity )
Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space.
Every normed vector space V sits as a dense subspace inside a Banach space ; this Banach space is essentially uniquely defined by V and is called the completion of V.

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

Every and obtained
* Duality: Every statement, theorem, or definition in category theory has a dual which is essentially obtained by " reversing all the arrows ".
Every gap sequence that contains 1 yields a correct sort ; however, the properties of thus obtained versions of Shellsort may be very different.
Every finite-dimensional inner product space has an orthonormal basis, which may be obtained from an arbitrary basis using the Gram – Schmidt process.
Every Boolean algebra can be obtained in this way from a suitable topological space: see Stone's representation theorem for Boolean algebras.
Every building has a canonical length metric inherited from the geometric realisation obtained by identifying the vertices with an orthonormal basis of a Hilbert space.
Every name lookup must either start with a query to a root server or use information that was once obtained from a root server.
Every such person whose Canadian parent or parents were also not born in Canada and obtained their citizenship at birth by descent ( second generation born abroad ) must have successfully applied to maintain their Canadian citizenship before their 28th birthday, that is, if their 28th birthday took place before 17 April 2009.
Every penny we obtained was immediately devoured by the expenses of the newspaper.
Every closed, orientable three-manifold may be so obtained ; this follows from deep results on the triangulability of three-manifolds due to Moise.
Every year, about 3, 000, 000 address changes are processed by Elections Canada from information obtained from the Canada Revenue Agency, Canada Post ( via the National Change of Address service ), provincial and territorial motor vehicle registrars, and provincial electoral agencies with permanent voters lists.
Every year, about 400, 000 Canadians reach voting age and 200, 000 Canadians die, resulting in changes to the National Register of Electors based on information obtained from the Canada Revenue Agency, provincial and territorial motor vehicle registrars, and provincial electoral agencies with permanent voters lists.
Every closed, orientable, connected 3-manifold is obtained by performing Dehn surgery on a link in the 3-sphere.
Every manifold has an underlying topological manifold, obtained simply by forgetting the additional structure.
Every non-singular rational surface can be obtained by repeatedly blowing up a minimal rational surface.
* Every continuous plurisubharmonic function can be obtained as a limit of monotonically decreasing sequence of smooth plurisubharmonic functions.

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