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Every open subgroup H is also closed, since the complement of H is the open set given by the union of open sets gH for g in G
Some Related Sentences
Every and open
Every night they all went to Mama and Papa Albright's, and sat on the open front porch, where they could get the breeze.
When coming to Kubla Khan, he pointed out: " instead of being content to have written finely under the influence of laudanum, recommends ' Kubla-Khan ' to his readers, not as a poem, but as ' a psychological curiosity ' ... Every lover of books, scholar or not, who knows what it is to have his quarto open against a loaf at his tea ... ought to be in possession of Mr. Coleridge's poems, if it is only for ' Christabel ', ' Kubla Khan ', and the ' Ancient Mariner '.
Every judgment contained the reasons behind the decision and the judges assenting ; if there was a dissenting judge, he was allowed to deliver his own judgment, with all judgments read in open court before the agents of the parties to the dispute.
Every day, doors seem to open, and every day, we interact, perhaps more than ever before, with the world outside.
Every map that is injective, continuous and either open or closed is an embedding ; however there are also embeddings which are neither open nor closed.
Every year, Eton employs a ' Director-in-Residence ', an external professional director on a one-year contract who normally directs one house play and the Lower Boy play ( a school play open solely to the first two year groups ), as well as teaching Drama and Theatre Studies to most year groups.
Every microwave oven sold has a protective interlock so that it cannot be run when the door is open or improperly latched.
Every Tuesday and Saturday mornings in the summer near the old train station a farmers ' market is open, where farmers sell their fresh goods.
Every week of the Michaelmas and Lent terms, and twice in Easter term, Churchill is host to Pav, a music event unusual for Cambridge events in that it is free and open to all university members.
Every mRNA consists of three parts-5 ' untranslated region ( 5 ' UTR ), protein-coding region or open reading frame ( ORF ) and 3 ' untranslated region ( 3 ' UTR ).
Every smooth manifold defined in this way has a natural diffeology, for which the plots correspond to the smooth maps from open subsets of R < sup > n </ sup > to the manifold.
Every summer, operas, music and drama are performed in the open air at the Freilichtbühne during the month-long Wetzlar Festival (" Wetzlarer Festspiele ").
Every year there is a famous cross-country ski race called the Engadin Skimarathon from Maloja, across the frozen lakes and over the open meadows and ending in S-chanf.
Every and subgroup
* Every closed subgroup of a profinite group is itself profinite ; the topology arising from the profiniteness agrees with the subspace topology.
* Every finitely generated group with a recursively enumerable presentation and insoluble word problem is a subgroup of a finitely presented group with insoluble word problem
Every subgroup of a topological group is itself a topological group when given the subspace topology.
Every subgroup of a free abelian group is itself free abelian, which is important for the description of a general abelian group as a cokernel of a homomorphism between free abelian groups.
Every group of prime order is cyclic, since Lagrange's theorem implies that the cyclic subgroup generated by
Iwasawa worked with so-called-extensions: infinite extensions of a number field with Galois group isomorphic to the additive group of p-adic integers for some prime p. Every closed subgroup of is of the form, so by Galois theory, a-extension is the same thing as a tower of fields such that.
* Every triangle group T is a discrete subgroup of the isometry group of the sphere ( when T is finite ), the Euclidean plane ( when T has a Z + Z subgroup of finite index ), or the hyperbolic plane.
Recall that a subsemigroup G of a semigroup S is a subgroup of S ( also called sometimes a group in S ) if there exists an idempotent e such that G is a group with identity element e. A semigroup S is group-bound if some power of each element of S lies in some subgroup of S. Every finite semigroup is group-bound, but a group-bound semigroup might be infinite.
Every subgroup is organized around a set of brothers, each of whom is often married to a group of sisters.
Every finite group is a subgroup of the mapping class group of a closed, orientable surface, moreover one can realize any finite group as the group of isometries of some compact Riemann surface.
Every proper subgroup of G can be assumed a solvable group, meaning that much theory of such subgroups could be applied.
Every quasinormal subgroup is a modular subgroup, that is, a modular element in the lattice of subgroups.
Every group has itself ( the improper subgroup ) and the trivial subgroup as two of its fully characteristic subgroups.
Every and H
Every homomorphism f: G → H of Lie groups induces a homomorphism between the corresponding Lie algebras and.
The last two lines of the Act IV-scene 2 funeral song may also have inspired the lines W. H. Auden, the librettist for Stravinsky's The Rake's Progress, puts into the mouth of Anne Truelove at the end of the opera: " Every wearied body must late or soon return to dust ".
Every adult citizen of this small settlement signed the small petition ; E. K Dyer and his wife, William Johnson, Joseph Otis and his wife, Hiram Walker and his wife, Joseph Pease and R. H. Valentine.
Every quantum mechanical observable corresponds to a unique function or distribution on phase space, and vice versa, as specified by Hermann Weyl ( 1927 ) and supplemented by John von Neumann ( 1931 ); Eugene Wigner ( 1932 ); and, in a grand synthesis, by H J Groenewold ( 1946 ).
Every H * is very special in structure: it is pure-injective ( also called algebraically compact ), which says more or less that solving equations in H * is relatively straightforward.
Every chain may run in the same direction to form a parallel sheet, every other chain may run in the reverse chemical direction to form an anti parallel sheet, or the chains may be parallel and anti parallel to form a mixed sheet. The pattern of H bonding is different in the parallel and anti parallel configurations.
* Every finite-dimensional simple algebra over R must be a matrix ring over R, C, or H. Every central simple algebra over R must be a matrix ring over R or H. These results follow from the Frobenius theorem.
Every graph has a harmonious coloring, since it suffices to assign every vertex a distinct color ; thus χ < sub > H </ sub >( G ) ≤ | V ( G )|.
Every morphism f: G → H in Grp has a category-theoretic kernel ( given by the ordinary kernel of algebra ker f =
Every polytype can have monoclinic ( M ) or hexagonal ( H ) symmetry, and therefore some sources label them, for example, not as 6C, but 6H or 6M depending on the symmetry.
Its publications include Every Stony Acre Has a Name: Celebration of the Townland in Ulster by Tony Canavan, and Townlands in Ulster: Local History Studies, edited by W. H.
She also provided a technical review of the educational text book " The Physics of Every Day Phenomena " by Thomas Griffith ( McGraw-Hill ), “ Physics for the Life Sciences " by Philip Kesten and David Tauk ( W. H.
Every sitting U. S. President since 1960 ( Eisenhower, John F. Kennedy, Lyndon B. Johnson, Richard Nixon, Gerald Ford, Jimmy Carter, Ronald Reagan, George H. W. Bush, Bill Clinton and George W. Bush ) has addressed a convention or attended an event at Cobo Center.
Every recent president has supported the power of impoundment including Presidents Ronald Reagan, George H. W. Bush, Bill Clinton, George W. Bush, and Barack Obama.
Every complete, connected, simply-connected manifold of constant negative curvature − 1 is isometric to the real hyperbolic space H < sup > n </ sup >.