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Page "Category (mathematics)" ¶ 19
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Any and group
* Any member of the genus Eunectes, a group of large, aquatic snakes found in South America
Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup.
Any formal or informal groupa family, a church, a club, a business, a trade union — may be said to have government.
* Any Lie group G defines an associated real Lie algebra.
* Any topologically closed subgroup of a Lie group is a Lie group.
* Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.
* Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.
Any Lie group G can be decomposed into discrete, simple, and abelian groups in a canonical way as follows.
# Any tangent vector at the identity of a Lie group can be extended to a left invariant vector field by left translating the tangent vector to other points of the manifold.
" Any attempt to organize the group ... under a single authority would eliminate their independent initiatives, and thus reduce their joint effectiveness to that of the single person directing them from the centre.
Any symmetry group whose elements have a common fixed point, which is true for all finite symmetry groups and also for the symmetry groups of bounded figures, can be represented as a subgroup of orthogonal group O ( n ) by choosing the origin to be a fixed point.
However, in the case of a finitely presented group we know that not all the generators can be trivial ( Any individual generator could be, of course ).
* Any subgroup of a free group is free.
Any group of four students may run for office, but there must always be four students.
Any group that managed to find ways of reasoning effectively would reap benefits for all its members, increasing their fitness.
Any time during a triad conversation, group members can switch seats and one of the co-pilots can sit in the pilot ’ s seat.

Any and can
He merely said, `` Any good decorator these days can make you a tasteful home ''.
Any alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.
Any reputable French interne can supply you with a dozen similar instances, and I'll presently recount a case out of my own personal experience, but, for the moment, let's resume our catalogue.
Any needy family living in San Francisco can obtain toys by writing to Christmas Toys, 676 Howard street, San Francisco 5, and listing the parent's name and address and the age and sex of each child in the family between the ages of 1 and 12.
Any breach of these laws is a criminal offence and can lead to fine of up to £ 5, 000 or six months in prison.
Any use of antibiotics can increase selective pressure in a population of bacteria to allow the resistant bacteria to thrive and the susceptible bacteria to die off.
* Any ring A can be considered as a Z-algebra in a unique way.
Any of these body styles can optionally incorporate a " cutaway ".
Any Latin-American country can join the 1980 Montevideo Treaty.
Any given bookmaker will weight their odds so that no one customer can cover all outcomes at a profit against their books.
Any node in the data structure can be reached by starting at root node and repeatedly following references to either the left or right child.
Any Banach algebra ( whether it has an identity element or not ) can be embedded isometrically into a unital Banach algebra so as to form a closed ideal of.
Any of these ways can be criticized for ...
* Any locally compact Hausdorff space can be turned into a compact space by adding a single point to it, by means of Alexandroff one-point compactification.
Any Sangiovese-based wine made according to the Chianti guidelines from these vineyards can be labelled and marked under the basic Chianti DOCG should the producer wish to use the designation.
Any units of angular measure can be used for declination, but it is customarily measured in the degrees ( ° ), minutes ( ' ), and seconds ( " ) of sexagesimal measure, with 90 ° equivalent to circle.
Any convex polyhedron can be distorted into a canonical form, in which a midsphere ( or intersphere ) exists tangent to every edge, such that the average position of these points is the center of the sphere, and this form is unique up to congruences.
Any person who uses the Spanish title of " Doctor " ( or " Dr .") without being included in this Government database can be prosecuted for fraud.
Any player on the kicking team behind the kicker, and including the kicker, can recover the kick.
Any sound that can be sampled can be used.
Any ellipse can be obtained by rotation and translation of a canonical ellipse with the proper semi-diameters.
# Any real number can be added to both sides.
# Any real number can be subtracted from both sides.
# Any real number can be multiplied to both sides.

Any and be
Any posse riding down the street to demand Blue Throat's surrender would be wiped out with one deadly burst of fire.
Any fee so determined shall be entered as a part of such award, and payment thereof shall be made by the Secretary of the Treasury by deducting the amount thereof from the total amount paid pursuant to the award.
Any agreement to the contrary shall be unlawful and void.
Any and all payments required to be made by the Secretary of the Treasury under this title pursuant to any award made by the Commission to the Government of the United States shall be covered into the Treasury to the credit of miscellaneous receipts.
Any claimant whose claim is denied, or is approved for less than the full amount of such claim, shall be entitled, under such regulations as the Commission may prescribe, to a hearing before the Commission, or its duly authorized representatives, with respect to such claim.
Any person who makes application for any such payment shall be held to have consented to all the provisions of this Title.
Any failure to file timely returns or make estimated tax payments when due must be fully explained.
Any irregularity on the piston heads will make it impossible, with normal means, to determine the final combustion chamber volume because the volume displaced by the piston heads cannot be readily computed.
Any fraction of an inch involved in the measurement must be converted to a decimal equivalent to simplify the mathematics.
Any house built now below that line without air conditioning will be obsolete in 10 years.
Any other point of intersection between C and Af will be called a tangent point.
Any free elections that were to be held in Poland would have to produce a government in which Moscow had complete confidence, and all pressure from the West for free voting by anti-Soviet elements in Poland would be met by restrictions on voting by these elements.
Any example of grand or exquisite diction may have been created by the poet who compiled numerous lays into the two works we possess or may be due to one of his completely unknown fellow-craftsmen.
Any flat-bed press capable of pressing a specimen 22 inches square may be used as an alternative.
Any retaliatory gas attack would be airborne.
Any animal could when travelin' fast, be sent heels over head by the simple process of overtakin' the brute, seizin' its tail, and givin' the latter a pull to one side.
Any number of other ways exist to be rich.
* Any large snake that " crushes " its prey ( see Constriction ), if applied loosely, could be called anaconda.
Any person or entity wishing to use intellectual property held under copyright must receive permission from the copyright holder to use this work, and often will be asked to pay for the use of copyrighted material.
Any information may be conveyed by an analog signal ; often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure.
Any historical material on anagrams must always be interpreted in terms of the assumptions and spellings that were current for the language in question.

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