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 net on X has a convergent subnet ( see the article on nets for a proof ).

# Every filter on X has a convergent refinement.

# Every ultrafilter on X converges to at least one point.

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

Every continuous map f: X → Y induces an algebra homomorphism C ( f ): C ( Y ) → C ( X ) by the rule C ( f )( φ ) = φ o f for every φ in C ( Y ).

* Every linear combination of its components Y = a < sub > 1 </ sub > X < sub > 1 </ sub > + … + a < sub > k </ sub > X < sub > k </ sub > is normally distributed.

Every significant section of roadway maintained by the state is assigned a number, officially State Highway Route X but commonly called Route X by the NJDOT and the general public.

Every variable X < sub > i </ sub > in the sequence is associated with a Bernoulli trial or experiment.

Every Gauss – Markov process X ( t ) possesses the three following properties:

Every time someone gave an answer that was not on the board, the family lose a life, accompanied by a large " X " on the board with the infamous " uh-uhh " sound.

Every sigma-ideal on X can be recovered in this way by placing a suitable measure on X, although the measure may be rather pathological.

* Every non-empty Baire space is of second category in itself, and every intersection of countably many dense open subsets of X is non-empty, but the converse of neither of these is true, as is shown by the topological disjoint sum of the rationals and the unit interval 1.

* Every cover is a local homeomorphism — that is, for every, there exists a neighborhood of c and a neighborhood of such that the restriction of p to U yields a homeomorphism from U to V. This implies that C and X share all local properties.

Every universal cover p: D → X is regular, with deck transformation group being isomorphic to the fundamental group.

Every cumulant is just μ times the corresponding cumulant of the constant random variable X = 1.

Every closed point of Hilb ( X ) corresponds to a closed subscheme of a fixed scheme X, and every closed subscheme is represented by such a point.

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

Every February, A. Y. S. O.

* Every Y is a Z.

* " There's a Little Bit of You in Every Love Song " w. E. Y. Harburg m. Sammy Fain.

# Every K3 surface is Kähler ( by a theorem of Y .- T. Siu ).

* " Every Day "-Cholos Cholas Y Pistolas ( 2005 )

* Every object Y can be embedded in a distinguished triangle with,