:“ Any linear map from V to an algebra A can be uniquely extended to an algebra homomorphism from T ( V ) to A .”

* quantification Any morphism f: X → Y in a category with pullbacks induces a monotonous map acting by pullbacks ( A monotonous map is a functor if we consider the preorders as categories ).

Any stereographic projection of a sphere onto a plane will produce one " point at infinity ", and it will map the lines of latitude and longitude on the sphere into circles and straight lines, respectively, in the plane.

* Any bilinear map is a multilinear map.

* Any continuous map of topological spaces determines a sheaf of sets.

Any covering space of a differentiable manifold may be equipped with a ( natural ) differentiable structure that turns p ( the covering map in question ) into a local diffeomorphism – a map with constant rank n.

A weight on a Lie algebra g over a field F is a linear map λ: g → F with λ ( y )= 0 for all x, y in g. Any weight on a Lie algebra g vanishes on the derived algebra and hence descends to a weight on the abelian Lie algebra g /.

Any map of the region demonstrates the tradition by the proliferation of " Sidi " s, showing places named after the marabouts.

Any proposed inverse R of F ( reconstruction formula, in the lingo ) would have to map to some subset of.

Any ring homomorphism A → B gives a map K < sub > 0 </ sub >( A ) → K < sub > 0 </ sub >( B ) by mapping ( the class of ) a projective A-module M to M ⊗< sub > A </ sub > B, making K < sub > 0 </ sub > a covariant functor.

Any tool that tries to simplify a complex picture will introduce distortions, whether it is a geographic map or a set of scenarios.

Any such field is either equal to K or is also rational, i. e. L = K ( F ) for some rational function F. In geometrical terms this states that a non-constant rational map from the projective line to a curve C can only occur when C also has genus 0.

Any linear map induces a conjugate linear map, defined by the formula

* Any irreducible representation R of H gives an irreducible representation of G using the quotient map from G to H ( that is, as a restricted representation ).

* Any map f: Y → X is null-homotopic.

The canonical ring and therefore likewise the Kodaira dimension is a birational invariant: Any birational map between smooth compact complex manifolds induces an isomorphism between the respective canonical rings.

A user-created map of the early General Any Topic forum.

A user-created map of the General Any Topic forums through FM's Napoleon wars.

A user-created map of the General Any Topic forums during its " industrial " era.

A user-created map of the General Any Topic forums during its Renaissance.

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 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 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 adjustments which are made, Mr. Grenier said earlier this month, will appear on the balance of the tax bill since most of the town's taxpayers take the option of paying quarterly with the balance due next year.

Any decline in amphibian numbers will have an impact on the patterns of predation.

Any historical material on anagrams must always be interpreted in terms of the assumptions and spellings that were current for the language in question.

Any player may declare the game over at any time during his turn if either of two conditions is true: one chain has 41 or more tiles, or there is at least one chain on the board and every chain on the board has 11 or more tiles.

Most of the C code being written nowadays is based on ANSI C. Any program written only in standard C and without any hardware dependent assumptions is virtually guaranteed to compile correctly on any platform with a conforming C implementation.

Any alcohol ( beer, wine, spirits ) cannot be bought on Sundays before noon.

Any player is usually allowed to control or bet in as many boxes as desired at a single table, but it is prohibited for an individual to play on more than one table at a time or to place multiple bets within a single box.

Any measure μ defined on the σ-algebra of Borel sets is called a Borel measure.

Any desired arbitration logic is placed on the daughter cards.

Any attempt to impose an organization on them is bound to be somewhat arbitrary.

Any differential area with normal vector of a given internal surface area, bounding a portion of the body, experiences a contact force arising from the contact between both portions of the body on each side of, and it is given by

The Environmental Modification Convention ( ENMOD ), formally the Convention on the Prohibition of Military or Any Other Hostile Use of Environmental Modification Techniques is an international treaty prohibiting the military or other hostile use of environmental modification techniques.

One episode in Series 5 of Steptoe and Son was entitled " Any Old Iron ", for the same reason, when Albert thinks that Harold is ' on the turn '.

Any piece of DNA with the point centromere DNA sequence on it will typically form a centomere if present in the appropriate species.

Any person who felt himself wronged might lay an information before the Council of Areopagus, on declaring what law was broken by the wrong done to him.

Any elected or appointed board, committee, town officer or ten voters, may place an article on the warrant.

Any rain falling on the above-water rim quickly percolates through the surface sand and encounters the salt water underneath.

* 1976 – The United Nations General Assembly adopts the Convention on the Prohibition of Military or Any Other Hostile Use of Environmental Modification Techniques.

Any player on the kicking team behind the kicker, and including the kicker, can recover the kick.

:* Any total order on X has exactly one equivalence class, X itself, because x ~ y for all x and y ;