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Every polyhedron, regular and irregular, convex and concave, has a dihedral angle at every edge.
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Every and polyhedron
Every convex centrally symmetric polyhedron P in R < sup > 3 </ sup > admits a pair of opposite ( antipodal ) points and a path of length L joining them and lying on the boundary ∂ P of P, satisfying
Every and regular
Every regular language is context-free, every context-free language, not containing the empty string, is context-sensitive and every context-sensitive language is recursive and every recursive language is recursively enumerable.
* Every locally compact regular space is completely regular, and therefore every locally compact Hausdorff space is Tychonoff.
Nordau saw in Jewish Emancipation the result of ' a regular equation: Every man is born with certain rights ; the Jews are human beings, consequently the Jews are born to own the rights of man.
Every such regular cover is a principal G-bundle, where G = Aut ( p ) is considered as a discrete topological group.
Every universal cover p: D → X is regular, with deck transformation group being isomorphic to the fundamental group.
Every fourth year when the games were also held, the festival was known as the " Great Panathenaia ," and was 3 or 4 days longer than the regular festival.
Every and convex
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 antiparallelogram has an isosceles trapezoid as its convex hull, and may be formed from the diagonals and non-parallel sides of an isosceles trapezoid.
: Every correspondence that maps a compact convex subset of a locally convex space into itself with a closed graph and convex nonempty images has a fixed point.
* Every locally convex topological vector space has a neighbourhood basis consisting of barrelled sets.
* Every metrisable locally convex space with continuous dual carries the Mackey topology, that is, or to put it more succinctly every Mackey space carries the Mackey topology
Every ( bounded ) convex polytope is the image of a simplex, as every point is a convex combination of the ( finitely many ) vertices.
Every and concave
Every and has
Every woman has had the experience of saying no when she meant yes, and saying yes when she meant no.
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 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.
Every community, if it is alive has a spirit, and that spirit is the center of its unity and identity.
Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set.
** 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.
The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
* 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 unit of length has a corresponding unit of area, namely the area of a square with the given side length.
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 ATM cell has an 8-or 12-bit Virtual Path Identifier ( VPI ) and 16-bit Virtual Channel Identifier ( VCI ) pair defined in its header.
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