** 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 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 Java 2D drawing operation can ultimately be treated as filling a shape using a paint and compositing the result onto the screen.

Every event aired on SETV is almost entirely ran by the students filling positions: Camera, Audio, Director, TD, Grips, Handheld, or Producer.

* Every quadratic Bézier curve is also a cubic Bézier curve, and more generally, every degree n Bézier curve is also a degree m curve for any m > n. In detail, a degree n curve with control points P < sub > 0 </ sub >, …, P < sub > n </ sub > is equivalent ( including the parametrization ) to the degree n + 1 curve with control points P '< sub > 0 </ sub >, …, P '< sub > n + 1 </ sub >, where.

Every point on the Lorenz curve represents a statement like " the bottom 20 % of all households have 10 % of the total income.

Every immersed curve in the plane admits two possible orientations.

Every study has found that instead of people's MBTI scores clustering around two opposite poles, such as intuition vs. sensation, with few people scoring in the middle, people's scores actually cluster around the middle of each scale in a bell curve.

Every Edwards curve with a point of order 3 can be written in the ways shown above.

Every algebraic curve C of genus g ≥ 1 is associated with an abelian variety J of dimension g, by means of an analytic map of C into J.

Every closed curve c on X is homologous to for some simple closed curves c < sub > i </ sub >, that is,

Every minimal projective ruled surface other than the projective plane is the projective bundle of a 2-dimensional vector bundle over some curve.

Every algebraic plane curve has a degree, which can be defined, in case of an algebraically closed field, as number of intersections of the curve with a generic line.

Every irreducible non-degenerate curve of degree is a rational normal curve.

Four other hits from the album made the Pop top 20: " Every Heartbeat " ( No. 2 ), " That's What Love Is For " ( No. 7 ), " Good For Me " ( No. 8 ), and " I Will Remember You " ( No. 20 ).

" With Every Heartbeat ", " Handle Me " and " Cobrastyle " were top ten club hits, and the former received airplay at US pop and dance radio stations.

Good Trouble ( 1982 ) and Wheels Are Turnin ' ( 1984 ) were follow-up albums which also did well commercially, the former containing the hit singles " Keep the Fire Burnin '" ( U. S. # 7 ), " Sweet Time " ( U. S. # 26 ) and the un-ranked " The Key " and the latter containing the # 1 hit single " Can't Fight This Feeling " plus three more hits: " I Do ' Wanna Know " ( U. S. # 29 ), " One Lonely Night " ( U. S. # 19 ), " Live Every Moment " ( U. S. # 34 ) and the un-ranked " Break His Spell ".

Released in 1988, the album launched five top ten hits on the Billboard Hot 100 including the number-one single, the self-penned " My Prerogative ", which became, along with " Every Little Step " and the title track, signature hits for the performer.

The album included the band's biggest hit, the No. 1 hit single " Every Rose Has Its Thorn ", along with other hits like: " Nothin ' but a Good Time ", " Fallen Angel ", and the Loggins and Messina cover " Your Mama Don't Dance ".

Although they never replicated their earlier success, the group did manage to score a few hits with " It's So Nice ( To Have You Home )" ( 1976 ), " I Wanna Go Back " ( 1977 ) and " Anthem ( One Day in Every Week )" ( 1978 ).

Subsequent albums shared this similar style, and the band landed a number of hits with " Every Morning ", " Someday ", and " When It's Over ".

Pernilla was one of Sweden's hottest talents, with hits including Svindlande affärer, I Need Your Love, Every Time When We're Together and Running for Cover.

Martino had four other US top 10 hits in 1963 and 1964-" Painted, Tainted Rose " ( 1963 ), " I Love You More and More Every Day ", " Tears and Roses " and " Silver Bells " ( all 1964 ).

Davis only achieved two other major country hits the rest of the decade, " Fuel to the Flame " ( written by Dolly Parton, whom Davis paid tribute to with an album called Skeeter Sings Dolly in 1972 ), and " There's a Fool Born Every Minute ".

Every Major League player with 2, 800 hits or more is presently enshrined in Cooperstown, with the following exceptions: Harold Baines, Pete Rose ( current hit record-holder, who is banned from appearing on the official ballot Rose earns write-in votes, they are declared invalid ); Rafael Palmeiro ; Craig Biggio, Ivan Rodriguez and Barry Bonds ( none of whom have been out of Major League Baseball for the prerequisite five years ); and Derek Jeter, Alex Rodriguez, and Omar Vizquel ( all of whom are still active ).

While Robert Lamm maintains his songwriting prowess on Chicago VI ( authoring half of the album's tracks, including his response to some of Chicago's negative reviewers in " Critics ' Choice "), it is James Pankow who is responsible for the album's two hits, " Just You ' N ' Me " (# 4 ) and " Feelin ' Stronger Every Day " (# 10 ), the last of which was co-composed with Peter Cetera, who, himself landed another track on Chicago VI, the country-influenced " In Terms Of Two ".

Later in the 1970s, Rabbitt helped to develop the crossover-influenced sound of country music prevalent in the 1980s with such hits as " Suspicions " and " Every Which Way but Loose.

Every day the online version receives tens of thousands of hits and the CD-ROM of the first edition now in its fourth updated distribution.

Three of the thirteen tracks from the combined vinyl / CD Best of Bee Gees do not appear amongst the forty seven tracks on Their Greatest Hits: The Record: " I Can't See Nobody " and " Every Christian Lion Hearted Man Will Show You " had only actually been the B-sides of other hits on Best of Bee Gees, while " Tomorrow, Tomorrow " had charted but had never reached the top 20 in the charts of the UK, USA nor Australia.

Her best-known recordings are the soul hits, " Every Little Bit Hurts ", When I'm Gone, and " You've Made Me So Very Happy.

Other artists with whom Ashford & Simpson had hits were Teddy Pendergrass (" Is It Still Good to You "), The Brothers Johnson (" Ride-O-Rocket "), Chaka Khan, both on her own (" I'm Every Woman " and " Clouds "), and with Rufus (" Keep It Comin '" and " Ain't Nothin ' But a Maybe ").

A combination of high production standards, the growing confidence of the main songwriting team of Wilson and Brown, and tight harmonies enabled them to secure further big hits such as " You Sexy Thing " and " Every 1's a Winner ", which were also U. S. hits, peaking at # 3 ( 1976 ) and # 6 ( 1979 ), respectively.

) The album was released throughout Europe, and there were big hits in Greece ( where Every Time was a No. 1 single ), Sweden, Norway and Holland.

Their hits include: " Time To Wonder ", " Every Generation Got Its Own Disease ", " Won't Forget These Days ", " Radio Orchid ", " Dancing in the Sunshine of the Dark ", " Milk & Honey ", and " Trapped Today, Trapped Tomorrow ".

In 1993, the band had its first international success with the hits Radio Orchid and Every Generation got its own Disease from the album Mono and successfully toured several European countries and the USA.

Fargo's 1978 album, Shame on Me also yielded two Top 10 hits, the title track and " Do I Love You ( Yes in Every Way )," which peaked at No. 2.