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Every non-empty intersection of a 3-sphere with a three-dimensional hyperplane is a 2-sphere ( unless the hyperplane is tangent to the 3-sphere, in which case the intersection is a single point ).

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## Some Related Sentences

Every and non-empty

** 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.
** Tukey's lemma:

__Every____non-empty__collection**of**finite character has**a**maximal element**with**respect**to**inclusion.
*

__Every____non-empty__set**of**left ideals**of**R**,**partially ordered by inclusion**,**has**a**maximal element**with**respect**to**set inclusion.
*

__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__

__non-empty__file must have at least one fork

**,**and depending on

**the**file system

**,**

**a**file may have one or more other associated forks

**,**

**which**

**in**turn may contain primary data integral

**to**

**the**file

**,**or just metadata.

Every and intersection

__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__ridge arises as

**the**

__intersection__

**of**two facets

**(**but

**the**

__intersection__

**of**two facets need not be

**a**ridge

**).**

__Every__outerplanar graph can be represented as an

__intersection__graph

**of**axis-aligned rectangles

**in**

**the**plane

**,**so outerplanar graphs have boxicity at most two.

__Every__

__intersection__

**with**

**a**state or US Highway on US 24 from

**the**Indiana state line

**to**I-475 at Toledo will be an interchange.

__Every__other interchange

**with**major roads along

**the**route

**(**Toorak

**,**Burke

**,**Tooronga and Warrigal Roads ) was an at-grade

__intersection__controlled by traffic-lights

**,**and because

**the**road was constructed through residential areas

**,**reduced speed limits were also enforced.

Every and 3-sphere

__Every__closed

**,**orientable

**,**connected 3-manifold

**is**obtained by performing Dehn surgery on

**a**link

**in**

**the**

__3-sphere__.

Every and with

__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__Wednesday night through Oct. 11 there will be an elaborate colored fountain display

**,**

__with__229 nozzles throwing jets

**of**water up

**to**130 feet.

__Every__unit

**of**length has

**a**corresponding unit

**of**area

**,**namely

**the**area

**of**

**a**square

__with__

**the**given side length.

* Revised Code

**of**Washington 9. 12. 010: "__Every__person who brings on his or her own behalf**,**or instigates**,**incites**,**or encourages another**to**bring**,**any false suit at law or**in**equity**in**any court**of**this state**,**__with__intent thereby**to**distress or harass**a**defendant**in****the**suit**,**or who serves or sends any paper or document purporting**to**be or resembling**a**judicial process**,**that**is**not**in**fact**a**judicial process**,****is**guilty**of****a**misdemeanor ; and**in****case****the**person offending**is**an attorney**,**he or she may**,****in**addition thereto be disbarred from practicing law within this state.__Every__Boolean algebra

**(**A

**,**∧, ∨) gives rise

**to**

**a**ring

**(**A

**,**+, ·) by defining

**a**+ b :=

**(**

**a**∧ ¬ b ) ∨

**(**b ∧ ¬

**a**) =

**(**

**a**∨ b ) ∧ ¬(

**a**∧ b )

**(**this operation

**is**called symmetric difference

**in**

**the**

**case**

**of**sets and XOR

**in**

**the**

**case**

**of**logic ) and

**a**· b :=

**a**∧ b. The zero element

**of**this ring coincides

__with__

**the**0

**of**

**the**Boolean algebra ;

**the**multiplicative identity element

**of**

**the**ring

**is**

**the**1

**of**

**the**Boolean algebra.

__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__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__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__commutative real unital Noetherian Banach algebra__with__no zero divisors**is**isomorphic**to****the**real or complex numbers.
Jimmy Hatlo's They'll Do It

__Every__Time was often displayed**in****a**two-panel format__with__**the**first panel showing some deceptive**,**pretentious**,**unwitting or scheming human behavior and**the**second panel revealing**the**truth**of****the**situation.__Every__year

**,**

**the**European Joint Conferences on Theory and Practice

**of**Software

**(**ETAPS ) sponsors

**the**International Conference on Compiler Construction

**(**CC ),

__with__papers from both

**the**academic and industrial sectors.

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__three years since Earnhardt's death**,**someone associated__with__Earnhardt has won**the**Daytona 500**(**his son Dale Earnhardt**,**Jr.**in**2004**,**Earnhardt's replacement Cup driver Kevin Harvick**in**2007**,**and Earnhardt Ganassi's Jamie McMurray**in**2010.
In Norse mythology

**,**Draupnir**(**Old Norse "**the**dripper ")**is****a**gold ring possessed by**the**god Odin__with__**the**ability**to**multiply itself:__Every__ninth night eight new rings ' drip ' from Draupnir**,**each one**of****the**same size and weight as**the**original.__Every__system must have

**a**class designated as " root ",

__with__one

**of**its creation procedures designated as " root procedure ".

Every and three-dimensional

__Every__improper rotation

**of**

__three-dimensional__Euclidean space

**is**rotation followed by

**a**reflection

**in**

**a**plane through

**the**origin.

1.687 seconds.