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Page "Tree (graph theory)" ¶ 30
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Every and finite
** Tukey's lemma: Every non-empty collection of finite character has a maximal element with respect to inclusion.
# Every open cover of A has a finite subcover.
* Countably compact: Every countable open cover has a finite subcover.
# Every finite and contingent being has a cause.
Every finite simple group is isomorphic to one of the following groups:
Hilbert's example: " the assertion that either there are only finitely many prime numbers or there are infinitely many " ( quoted in Davis 2000: 97 ); and Brouwer's: " Every mathematical species is either finite or infinite.
* Every finite topological space gives rise to a preorder on its points, in which x ≤ y if and only if x belongs to every neighborhood of y, and every finite preorder can be formed as the specialization preorder of a topological space in this way.
Every finite tree structure has a member that has no superior.
Every rational number / has two closely related expressions as a finite continued fraction, whose coefficients can be determined by applying the Euclidean algorithm to.
Every finite group of exponent n with m generators is a homomorphic image of B < sub > 0 </ sub >( m, n ).
Every known Sierpinski number k has a small covering set, a finite set of primes with at least one dividing k · 2 < sup > n </ sup >+ 1 for each n > 0.
Every finite-dimensional Hausdorff topological vector space is reflexive, because J is bijective by linear algebra, and because there is a unique Hausdorff vector space topology on a finite dimensional vector space.
: Every oriented prime closed 3-manifold can be cut along tori, so that the interior of each of the resulting manifolds has a geometric structure with finite volume.
Every finite or bounded interval of the real numbers that contains an infinite number of points must have at least one point of accumulation.
Every field of either type can be realized as the field of fractions of a Dedekind domain in which every non-zero ideal is of finite index.
Every process involving charged particles emits infinitely many coherent photons of infinite wavelength, and the amplitude for emitting any finite number of photons is zero.
Every finite group has a composition series, but not every infinite group has one.
* Every finite or cofinite subset of the natural numbers is computable.
* Every subset of may be covered by a finite set of positive orthants, whose apexes all belong to
* Every finite subextension of F / k is separable.
Every finite ordinal ( natural number ) is initial, but most infinite ordinals are not initial.
* Every finite-dimensional central simple algebra over a finite field must be a matrix ring over that field.
* Every commutative semisimple ring must be a finite direct product of fields.

Every and tree
Every morning early, in the summer, we searched the trunks of the trees as high as we could reach for the locust shells, carefully detached their hooked claws from the bark where they hung, and stabled them, a weird faery herd, in an angle between the high roots of the tulip tree, where no grass grew in the dense shade.
Every tree that is scorched and each bird nest that is devoured is a sign of the abiotic stress.
Every McIntosh apple has a direct lineage to a single tree discovered in 1796 by John McIntosh on his farm in Dundela, a hamlet near Morrisburg, in Dundas County, Ontario, Canada.
* Every tree is a bipartite graph and a median graph.
Every tree with only countably many vertices is a planar graph.
* Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.
* Every connected graph with only countably many vertices admits a normal spanning tree.
Every December, the city holds a Festival of Trees in the ice skating rink and the Tree Lighting Ceremony in which residents of Vacaville gather in downtown to see a tree illuminate and enjoy festive music played by the amazing Jepson Band, hot chocolate, and horse-drawn carriage rides.
Every year, a huge tree would be shipped from the Pacific Northwest to Lantana by rail to the grounds of the National Enquirer, adjacent to the Florida East Coast Railway tracks.
And finally, the residents pleaded that “ Every tree that can possibly be saved must be saved .” And so, in came the construction crews.
Every cover features the same image of a tree ( held to represent that " all is life "), and on the back the phrase: " time is the invention of men incapable of love ".
Every time the tree was destroyed, a new tree was planted at the same place.
* Every tree is bipartite.
Every year a thousand new branches spring up from that tree and all kinds of seeds hang on those branches and all those seeds become ripe.
Every night during the Christmas season, thousands of visitors would come to see the tree.
Every graph ( that is connected and not a tree ) has multiple spanning trees, so we once again have an example where the problem itself allows multiple possible outcomes, and the algorithm chosen can arrive at any one of them, but will never arrive at something else.
Every Christmas, Victoria Square forms the centrepiece for the Frankfurt Christmas Market and Craft Fair which also extends into New Street and abuts onto a craft fair in Chamberlain Square, with the city's official Christmas tree, donated each year by Sandvik, also standing in the square.
Every year the town erects a public Christmas tree and every child, local or visitor, is given a present.
Every year the lights are switched on in the Thoroughfare and then people gather near St Mary's to see the Christmas tree being lit up.
Every tree indigenous to Minnesota is grown in the Linnaeus Arboretum.
Every tree was stained with sacrificial blood.

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